Head of Department
Position: Head of Department & Lecturer
Tel: +27 (021) 959 3028
Tel: +27 (021) 959 3028
Bio:
Dr. Deon Solomons is a graduate of the University of Cape Town. He specializes in Mathematics and Applied Mathematics. From 2003 to 2006 and again in from 2015 to 2016 he taught undergraduate subjects in Mathematics, Statistics and Physics at Cape Peninsula University of Technology. From 2007 until 2014, he taught subjects in the Mathematics and Applied Mathematics at University of Cape Town. He joined the Department of Mathematics and Applied Mathematics at the University of the Western Cape in July 2016. He currently teaches Mathematics at undergraduate and Honours level. He has published in various international journals. He has performed research in Gravitation and Cosmology, as well as Biotechnology, applying analytical and numerical techniques to solve partial differential equations in fluid mechanics. His current research interests are Differential Geometry, Gravitation, and Cosmology.Academic Staff
Position: Associate Professor & Deputy Head of Department
Tel: +27 (021) 959 3436
Fax: +27 (021) 959 1241
Email: jmunyakazi@uwc.ac.za
He obtained a degree in Mathematics and Education from the Institut Supérieur Pédagogique de Bukavu (in the Democratic Republic of Congo) and served as a high school teacher of Mathematics in several schools in the African Great Lakes region from 1991 to 2003. He enrolled with the University of Stellenbosch to study for a postgraduate diploma in mathematical sciences at the African
Institute for Mathematical Sciences (AIMS) in September 2003. He completed his Masters and PhD degrees t the University of the Western Cape in 2006 and 2009, respectively.
Justin’s research interests include numerical methods for differential and integro-differential, scientific computing and applications of mathematics in biology. His current projects include
1) Higher order numerical methods for singularly perturbed systems of differential equations,
2) Design, analysis and implementation of numerical methods for integro-differential equations
3) Mathematical epidemiology and analysis of malaria enhancer and reducer factors.
Tel: +27 (021) 959 3436
Fax: +27 (021) 959 1241
Email: jmunyakazi@uwc.ac.za
Bio:
Justin Munyakazi is an Associate Professor in the Department of Mathematics and Applied Mathematics. He teaches at both undergraduate and postgraduate levels. He also supervises MSc and PhD students in the area of Numerical Analysis and Mathematical Biology.He obtained a degree in Mathematics and Education from the Institut Supérieur Pédagogique de Bukavu (in the Democratic Republic of Congo) and served as a high school teacher of Mathematics in several schools in the African Great Lakes region from 1991 to 2003. He enrolled with the University of Stellenbosch to study for a postgraduate diploma in mathematical sciences at the African
Institute for Mathematical Sciences (AIMS) in September 2003. He completed his Masters and PhD degrees t the University of the Western Cape in 2006 and 2009, respectively.
Justin’s research interests include numerical methods for differential and integro-differential, scientific computing and applications of mathematics in biology. His current projects include
1) Higher order numerical methods for singularly perturbed systems of differential equations,
2) Design, analysis and implementation of numerical methods for integro-differential equations
3) Mathematical epidemiology and analysis of malaria enhancer and reducer factors.
Position: Senior Professor (Department of Mathematics and Applied Mathematics)
Tel: 021 959 3917
Fax:
Email: kpatidar@uwc.ac.za
Biography:
Professor Patidar received his PhD (Mathematics) in 2002 from the Indian Institute of Technology (IIT) Kanpur -- a premier higher educational institute in India. He visited the universities of Tübingen (Germany) and Pretoria (South Africa) for his post-doctoral studies. Subsequently, he joined the University of the Western Cape (South Africa) in 2006 as a senior lecturer and currently holds the position of Senior Professor of Mathematics. He received a C1 rating from the South African National Research Foundation (NRF) for the period 2022-2027. Prior to this, he held a C2 rating for the periods 2010-2015 and 2016-2021. Professor Patidar was the principal investigator for the grants: NRF Focus Area Programme in Mathematics (2007-2008), NRF Competitive Programme for Rated Researchers (2010-2012, 2014-2016, 2017-2019 and 2021-2023) and NRF Programme Knowledge Interchange and Collaboration (2010, 2016).
Professor Patidar’s research involves mathematical methods and scientific computing for application problems that arise from the interactions between natural and life sciences as well as those from the engineering domain. His research involves analytical investigations and numerical experiments using finite difference, finite element, spline approximation and spectral methods for parameter sensitive differential models. He published more than 100 research articles (in journals of international standing), 6 invited book chapters, 12 papers in the proceedings of international conferences and 5 extended abstracts. He graduated 22 PhD and 18 MSc students under his supervision and currently supervising several students. He also acted as an external examiner for PhD theses from local as well as institutions abroad. Some of his accomplished and ongoing well-funded research projects include:
The development of reliable numerical methods for the mathematical models arising in population biology.
The development of efficient numerical methods for option pricing problems in computational finance.
Construction, analysis and implementation of numerical methods for singular perturbation problems.
High order numerical methods for singular perturbation problems.
Administration & Institutional Leadership:
Deputy Dean: Post-Graduate Studies: June 2021 – May 2024.
Acting Deputy Dean: Post-Graduate Studies: Nov 2020 - May 2021.
Head [Department of Mathematics and Applied Mathematics, UWC]: 2018 - 2020; 2021 - 2023.
Member of the Joint Appointments and Promotions Committee of Senate and Council, UWC: 2019, 2021, 2023.
Member of the Management Committee, Faculty of Natural Sciences, UWC: 2018 - 2020, 2021 - 2023.
Deputy Head [Department of Mathematics and Applied Mathematics, UWC]: 2014 - 2017.
Senate Research Committee [Representative from Science Faculty]: July 2013 - Dec 2015.
Senate Scholarships and Fellowships Committee [Representative from Science Faculty]: 2014-2019.
Member of the Executive Team of AIMS (African Institute for Mathematical Sciences) South Africa: 2015-2017; 2018-2020.
Deputy Chair of Science Faculty's Higher Degrees Committee: 2015-2017.
Member of the Executive Committee of Science Faculty's Higher Degrees Committee: 2014-2020.
Member of the Executive Committee of Science Faculty's Post-Graduate Committee: 2011-2013.
Member of Science Faculty's Professorial Appointments/Promotions Committee: 2015- .
Member of the Post-Graduate Committee of the Science Faculty, UWC: 2008-2013.
Member of the Appointment Committee of the Science Faculty, UWC: 2008.
Convener of departmental sub-committees [Library committee 2006-2008; Post-Graduate Studies committee 2008-2013].
Publications:
Summary as of 28 January 2024: Google Scholar Citations: 2439; h-index: 26; i10-index: 62. MathSciNet (Publications: 101; Citations: 453).
Invited book chapters: 6
Research papers in the peer reviewed international journals: 103.
Publications in Conference proceedings: 12
Extended Abstracts: 5.
Further details:
Book Chapters:
E. Ngounda, K.C. Patidar and E. Pindza, Pricing Barrier Options Using Integral Transforms, in B. Toni (ed.), New Trends and Advanced Methods in Interdisciplinary Mathematical Sciences, Springer International Publishing AG, Switzerland, 2017, 221-239.
E.B.M. Bashier and K.C. Patidar, A comparison of numerical methods for systems of first order delay differential equations arising in biology, In: F. Nyabadza, M. Kgosimore and E.M. Lungu (eds.), A Treatise of Biological Models, Nova Science Publishers, Inc., USA, 2012, 75-96.
Application of geometric explicit Runge-Kutta methods to pharmacokinetic models (with M.A. Akanbi), in K.J. Engemann, A.M. Gil-Lafuente and J.M. Merigo (eds.), Modeling and Simulation in Engineering, Economics and Management, Lecture Notes in Business Information Processing, Vol. 115, Springer-Verlag, Berlin, 2012, 259-269.
K.C. Patidar, Numerical methods for multi-parameter singular perturbation problems, in A. Abdulle, J. Banasiak, A. Damlamian and M. Sango (eds.): Multiple Scales Problems in Biomathematics, Mechanics, Physics and Numerics, GAKUTO International Series, Math. Sci. Appl., 31, 327-344, 2009.
J.M.-S. Lubuma and K.C. Patidar, Contributions to the theory of non-standard finite difference methods and applications to singular perturbation problems, Advances in the Applications of Nonstandard Finite Difference Schemes, R.E. Mickens (ed.), World Scientific, Singapore, 2005, 513-560.
A.B. Gumel, K.C. Patidar and R.J. Spiteri, Asymptotically consistent non-standard finite-difference methods for solving mathematical models arising in population biology, Advances in the Applications of Nonstandard Finite Difference Schemes, R.E. Mickens (ed.), World Scientific, Singapore, 2005, 385-421.
Research Papers:
S.M. Nuugulu, F. Gideon and K.C. Patidar, An efficient numerical method for pricing double-barrier
options on an underlying stock governed by a fractal stochastic process, Fractal & Fractional 7 (389) (2023) 15pp. DOI: https://doi.org/10.3390/fractalfract7050389.
C.K. Mbayi, J.B. Munyakazi and K.C. Patidar, A fitted numerical method for interior-layer paraboli convection-diffusion problems, International Journal of Computational Methods 19(10) (2022), Paper no. 2250028, 24 pp.
C.K. Mbayi, J.B. Munyakazi and K.C. Patidar, Layer resolving fitted mesh method for parabolic convection-diffusion problems with a variable diffusion, Journal of Applied Mathematics and Computing, 68 (2022) 1245–1270.
K.M. Owolabi, K.C. Patidar and A. Shikongo, A fitted operator method for a system of delay model of tumor cells dynamics within their micro-environment, Applied Mathematics & Information Sciences, 16 (2) (2022) 367-388.
Kailash C. Patidar and Andriamihaja Ramanantoanina, A non-standard finite difference scheme for a class of predator-prey systems with non-monotonic functional response, Journal of Difference Equations and Applications, 27(9) (2021) 1310-1328.
Elias M. Adamu, Kailash C. Patidar and Andriamihaja Ramanantoanina, An unconditionally stable nonstandard finite difference method to solve a mathematical model describing Visceral Leishmaniasis, Mathematics and Computers in Simulation 187 (2021) 171-190.
S.M. Nuugulu, F. Gideon and K.C. Patidar, A robust numerical scheme for a time fractional Black-Scholes partial differential equation describing stock exchange dynamics, Chaos, Solitons & Fractals 145 (2021) 110753.
S.M. Nuugulu, F. Gideon and K.C. Patidar, A robust numerical solution to a time-fractional Black-Scholes Equation, Advances in Difference Equations 123 (2021), 25pp.
M. Dube and K.C. Patidar, A robust nonstandard finite difference scheme for pricing real estate index options, Journal of Difference Equations and Applications 26 (11-12) (2020) 1471-1493.
W.D. Mergia and K.C. Patidar, High-order semi-implicit linear multistep LG scheme for a three species competition-diffusion system in two-dimensional spatial domain arising in ecology, Communications in Nonlinear Science and Numerical Simulation 84 (2020) 1-16.
C.K. Mbayi, J.B. Munyakazi and K.C. Patidar, A robust fitted numerical method for singularly perturbed turning point problems whose solution exhibits an interior layer, Quaestiones Mathematicae 43(1) (2020) 1-24.
K.M. Owolabi, K.C. Patidar and A. Shikongo, Robust numerical method for a tumor-host model with chemotherapy application, Mathematics in Engineering, Science and Aerospace 11(4) (2020) 739-764.
K.M. Owolabi, K.C. Patidar and A. Shikongo, A fitted operator method for model arising in vascular tumor dynamics, Communications in Mathematical Biology and Neuroscience 2020:4 (2020) 1-21.
K.M. Owolabi, K.C. Patidar and A. Shikongo, Efficient numerical method for a model arising in biological stoichiometry of tumour dynamics, Discrete & Continuous Dynamical Systems - Series S 12(3) (2019) 591-613.
K.M. Owolabi, K.C. Patidar and A. Shikongo, Numerical solution for a problem arising in angiogenic signalling, AIMS Mathematics 4(1) (2019) 43-63.
K.M. Owolabi, K.C. Patidar and A. Shikongo, A fitted numerical method for a model arising in HIV related cancer-immune system dynamics, Communications in Mathematical Biology and Neuroscience 2019 (2019) 1-23.
K.M. Owolabi, K.C. Patidar and A. Shikongo, A fitted operator method for tumor cells dynamics in their micro-environment, Communications in Mathematical Biology and Neuroscience 2019 (2019) 1-44.
J.B. Munyakazi, K.C. Patidar and M.T. Sayi, A fitted numerical method for parabolic turning point singularly perturbed problems with an interior layer, Numerical Methods Partial Differential Equations 35 (6) (2019) 2407-2422.
J.B. Munyakazi, K.C. Patidar and M.T. Sayi, A robust fitted operator finite difference method for singularly perturbed problems whose solution has an interior layer, Mathematics and Computers in Simulation 160 (2019) 155-167.
E. Pindza and K.C. Patidar, A robust spectral method for pricing of American put options on zero-coupon bonds, East Asian Journal on Applied Mathematics 8(1) (2018) 126-138.
W.D. Mergia and K.C. Patidar, Fractional-step $\theta$-method for solving singularly perturbed problem in ecology, Advances in Computational Mathematics 44(3) (2018) 645-671.
K.M. Owolabi, K.C. Patidar and A. Shikongo, Mathematical analysis and numerical simulation of a tumor-host model with chemotherapy application, Communications in Mathematical Biology and Neuroscience 2018 (2018), Article ID 21.
H.A. Obaid, R. Ouifki and K.C. Patidar, A nonstandard finite difference method for solving a mathematical model of HIV-TB co-infection, Journal of Difference Equations and Applications 23(6) (2017) 1105-1132.
E. Pindza, K.M. Owolabi and K.C. Patidar, Barycentric Jacobi spectral method for numerical solutions of the generalized Burgers-Huxley equation, International Journal of Nonlinear Sciences and Numerical Simulation 18(1) (2017) 67-81.
E.B.M. Bashier and K.C. Patidar, Optimal control of an epidemiological model with multiple time delays, Applied Mathematics and Computation 292(1) (2017) 47-56.
K.C. Patidar, Nonstandard finite difference methods: recent trends and further developments, Journal of Difference Equations and Applications 22(6) (2016) 817-849.
W.D. Mergia and K.C. Patidar, Efficient simulation of a slow-fast dynamical system using multirate finite difference schemes, Quaestiones Mathematicae 39(5) (2016) 689-714.
K.C. Patidar, S.K. Datta, T. Biswas and C. Biswas, On comparative growth relationship of iterated entire functions from the view point of slowly changing functions, Facta Universitatis (NIS), Series: Mathematics and Informatics 31(1) (2016) 139-159.
A.M.A. Adam, E.B.M. Bashier, M.H.A. Hashim and K.C. Patidar, Fitted Galerkin spectral method to solve delay partial differential equations, Mathematical Methods in the Applied Sciences 39 (2016) 3102-3115.
G. Buzuzi, J.B. Munyakazi and K.C. Patidar, A fitted numerical method to investigate the effect of various parameters on an MHD flow over an inclined plate, Numerical Methods for Partial Differential Equations 32(1) (2016) 106-120.
K.M. Owolabi and K.C. Patidar, Numerical simulations of multicomponent ecological models with adaptive methods, Theoretical Biology and Medical Modelling 13(1) (2016) 1-25. DOI: 10.1186/s12976-016-0027-4.
K.M. Owolabi and K.C. Patidar, Effect of spatial configuration of an extended nonlinear Kierstead-Slobodkin reaction-transport model with adaptive numerical scheme, SpringerPlus 5(303) (2016) 1-18. DOI: 10.1186/s40064-016-1941-y.
K.M. Owolabi and K.C. Patidar, On the Numerical Exploration of Burgers-Fisher Equation using Robust Implicit-Explicit Schemes, Transylvanian Review 24(6) (2016) 496-508.
K.M. Owolabi and K.C. Patidar, Robust numerical simulation of nonlinear stiff higher-order PDEs, Transylvanian Review 24(6) (2016) 509-526.
H.A. Obaid, R. Ouifki and K.C. Patidar, Analysis of an HIV model with distributed delay and behavior change, International Journal of Bio-mathematics 8(2) (2015). DOI: 10.1142/S1793524515500175.
J.B. Munyakazi and K.C. Patidar, A new fitted operator finite difference method to solve systems of evolutionary reaction-diffusion equations, Quaestiones Mathematicae 38(1) (2015) 121-138.
K.M. Owolabi and K.C. Patidar, Existence and permanence in a diffusive KiSS model with robust numerical simulations, International Journal of Differential Equations 2015, Article ID 485860, 8 pages.
P.K. Rallabandi and K.C. Patidar, A hybrid system of hidden Markov models and recurrent neural networks for learning deterministic finite state automata, International Journal of Computer, Electrical, Automation, Control and Information Engineering 9(11) (2015) 2078-2085.
S. Abbas, D. Bahuguna, E.B.M. Bashier and K.C. Patidar, Pseudo almost periodic mild solutions of quasilinear functional differential equations with application to mathematical biology, Neural, Parallel & Scientific Computations 23 (2015) 318-334.
E. Ngounda and K.C. Patidar, Limitations and improvements of standard spectral methods for pricing standard options, International Journal of Advances in Engineering Sciences and Applied Mathematics 7(3) (2015) 106-113.
E. Pindza, K.C. Patidar and E. Ngounda, Robust spectral method for numerical valuation of European options under Merton's jump-diffusion model, Numerical Methods for Partial Differential Equations 30 (2014) 1169-1188.
S.M.A.S. Elsheikh, K.C. Patidar and R. Ouifki, Analysis of a Malaria model with a distributed delay, IMA Journal of Applied Mathematics 79(6) (2014) 1139-1160.
S.M.A.S. Elsheikh, R. Ouifki and K.C. Patidar, A nonstandard finite difference method to solve a model of HIV-Malaria co-infection, Journal of Difference Equations and Applications 20(3) (2014) 354-378.
E. Ngounda, K.C. Patidar and E. Pindza, A robust spectral method for solving Heston's model, Journal of Optimization Theory and Applications 161(1) (2014) 164-178.
K.M. Owolabi and K.C. Patidar, Higher-order time-stepping methods for time-dependent reaction-diffusion equations arising in biology, Applied Mathematics and Computation 240(1) (2014) 30-50.
K.M. Owolabi and K.C. Patidar, Numerical solution of singular patterns in one-dimensional Gray-Scott-like models, International Journal of Nonlinear Sciences and Numerical Simulation 15(7-8) (2014) 437-462.
J.B. Munyakazi and K.C. Patidar, Performance of Richardson extrapolation on some numerical methods for a singularly perturbed turning point problem whose solution has boundary layers, Journal of the Korean Mathematical Society 51(4) (2014) 679-702.
M.H.M. Khabir and K.C. Patidar, Comparison of some numerical methods for option pricing problems, Neural, Parallel, and Scientific Computations 22 (2014) 521-538.
E. Pindza, K.C. Patidar and E. Ngounda, Implicit-explicit predictor-corrector methods combined with improved spectral methods for pricing European style vanilla and exotic options, Electronic Transactions on Numerical Analysis 40 (2013) 268-293.
E. Ngounda, K.C. Patidar and E. Pindza, Contour integral method for European options with jumps, Communications in Nonlinear Science and Numerical Simulation 18 (2013) 478-492.
E. Pindza and K.C. Patidar, A comparative performance of exponential time differencing and implicit explicit methods for pricing European options under the Black-Scholes and Merton jump-diffusion models, Review of the Bulletin of Calcutta Mathematical Society 21(1) (2013) 51-70.
H.A. Obaid, R. Ouifki and K.C. Patidar, An unconditionally stable nonstandard finite difference methods applied to a mathematical model of HIV infection, International Journal of Applied Mathematics and Computer Science 23(2) (2013) 357-372.
E.B.M. Bashier and K.C. Patidar, An efficient fitted operator method to solve delayed singularly perturbed differential-difference equations, Neural, Parallel & Scientific Computations 21 (2013) 217-234.
K.K. Sharma, P. Rai and K.C. Patidar, A review on singularly perturbed differential equations with turning points and interior layers, Applied Mathematics and Computation 219(22) (2013) 10575-10609.
J.B. Munyakazi and K.C. Patidar, A fitted numerical method for singularly perturbed parabolic reaction-diffusion problems, Computational and Applied Mathematics 32 (2013) 509-519.
MHM Khabir and KC Patidar, Spline approximation method to solve an option pricing problem, Journal of Difference Equations and Applications, 18(11) (2012) 1801-1816.
W. Mudzimbabwe, K.C. Patidar and P.J. Witbooi, European basket option pricing by maximizing over a subset of lower bounds, Quaestiones Mathematicae 35(2) (2012) 507-520.
JB Munyakazi and KC Patidar, Novel fitted operator finite difference methods for singularly perturbed elliptic convection-diffusion problems in two dimensions, Journal of Difference Equations and Applications, 18(5) (2012) 799-813.
W Mudzimbabwe, KC Patidar and PJ Witbooi, A reliable numerical method to price arithmetic Asian options, Applied Mathematics and Computation, 218(22) (2012), 10934-10942.
JB Munyakazi and KC Patidar, An efficient numerical method for a system of singularly perturbed reaction-diffusion equations, Neural, Parallel & Scientific Computations 20 (2012) 173-190.
I Ahmed I, PJ Witbooi and KC Patidar, Modeling the dynamics of an epidemic under vaccination in two interacting populations, Journal of Applied Mathematics, Published online. 14 pages. DOI:10.1155/2012/275902.
E.B.M. Bashier and K.C. Patidar, A fitted numerical method for a system of partial delay differential equations, Computers and Mathematics with Applications 61(6) (2011) 1475-1492.
E.B.M. Bashier and K.C. Patidar, A novel fitted operator finite difference method for a singularly perturbed delay parabolic partial differential equation, Applied Mathematics and Computation 217 (2011) 4728-4739.
E.B.M. Bashier and K.C. Patidar, A second order fitted operator finite difference method for a singularly perturbed delay parabolic partial differential equation, Journal of Difference Equations and Applications 17(5) (2011) 779-794.
K.C. Patidar, A new class of finite element method for convection-diffusion-reaction problems, Neural, Parallel & Scientific Computations 18(2) (2010) 237-252.
E.B.M. Bashier and K.C. Patidar, An almost second order fitted mesh numerical method for a singularly perturbed delay parabolic partial differential equation, Neural, Parallel & Scientific Computations 18(2) (2010) 137-154.
M.K. Kadalbajoo and K.C. Patidar, Variable mesh spline approximation method for solving singularly perturbed turning point problems having interior layer, Neural, Parallel & Scientific Computations 18(2) (2010) 207-220.
J.B. Munyakazi and K.C. Patidar, Higher order numerical methods for singularly perturbed elliptic problems, Neural, Parallel & Scientific Computations 18(1) (2010) 75-88.
J.B. Munyakazi and K.C. Patidar, Limitations of Richardson's extrapolation for a high order fitted mesh method for self-adjoint singularly perturbed problems, Journal of Applied Mathematics and Computing 32(1) (2010) 219-236.
J.M.-S. Lubuma and K.C. Patidar, Reliable finite element methods for self-adjoint singular perturbation problems, Quaestiones Mathematicae, 32(3) (2009) 397-413.
J.M.-S. Lubuma and K.C. Patidar, Towards the implementation of the singular function method for singular perturbation problems, Applied Mathematics and Computations 209 (1) (2009) 68-74.
K.C. Patidar, A robust fitted operator finite difference method for a two-parameter singular perturbation problem, Journal of Difference Equations and Applications 14 (12) (2008) 1197-1214.
J.B. Munyakazi and K.C. Patidar, On Richardson extrapolation for fitted operator finite difference methods, Applied Mathematics and Computations 201(1-2) (2008) 465-480.
C. Le Roux and K.C. Patidar, On the flow of a generalized Burgers fluid in an orthogonal rheometer, Nonlinear Analysis Series B: Real World Applications 9(5) (2008) 1882-1893.
S. Abelman and K.C. Patidar, Comparison of some recent numerical methods for initial value problems for stiff ordinary differential equations, Computers and Mathematics with Applications 55(4) (2008) 733-744.
K.C. Patidar, High order parameter uniform numerical method for singular perturbation problems, Applied Mathematics and Computation 188 (2007) 720-733.
K.C. Patidar and A. Shikongo, The applications of asymptotic analysis for developing reliable numerical method for a model singular perturbation problem, Journal of Numerical Analysis Industrial and Applied Mathematics 2(3-4) (2007) 193-207.
J.M.-S. Lubuma and K.C. Patidar, Solving singularly perturbed advection reaction equation via non-standard finite difference methods, Mathematical Methods in the Applied Sciences 30(14) (2007) 1627-1637.
J.M.-S. Lubuma and K.C. Patidar, $\varepsilon$-uniform non-standard finite difference methods for singularly perturbed nonlinear boundary value problems, Advances in Mathematical Sciences and Applications 17(2) (2007) 651-665.
J.M.-S. Lubuma and K.C. Patidar, Non-standard methods for singularly perturbed problems possessing oscillatory/layer solutions, Applied Mathematics and Computation 187 (2007) 1147-1160.
K.C. Patidar and K. K. Sharma, Uniformly convergent nonstandard finite difference methods for singularly perturbed differential difference equations with delay and advance, International Journal for Numerical Methods in Engineering 66 (2006) 272-296.
M.K. Kadalbajoo, K.C. Patidar and K. K. Sharma, $\varepsilon$-uniformly convergent fitted methods for the numerical solution of the problems arising from singularly perturbed general DDEs, Applied Mathematics and Computation 182 (2006) 119-139.
J.M.-S. Lubuma and K.C. Patidar, Uniformly convergent non-standard finite difference methods for self-adjoint singular perturbation problems, Journal of Computational and Applied Mathematics 191 (2006) 229-238.
K.C. Patidar and K. K. Sharma, $\varepsilon$-uniformly convergent non-standard finite difference methods for singularly perturbed differential difference equations with small delay, Applied Mathematics and Computation 175 (2006) 864-890.
M.K. Kadalbajoo and K.C. Patidar, $\varepsilon$-uniformly convergent fitted mesh finite difference methods for general singular perturbation problems, Applied Mathematics and Computation 179 (2006) 248-266.
K.C. Patidar, On the use of non-standard finite difference methods, Journal of Difference Equations and Applications 11 (2005) 735-758.
K.C. Patidar, High order fitted operator numerical method for the self-adjoint singular perturbation problems, Applied Mathematics and Computation 171(1) (2005) 547-566.
K.C. Patidar, Dispersion induced by the pollution for the wave equation, Applied Mathematics and Computation 160 (2005) 329-341.
K.C. Patidar, Pollution free discretization of the wave equation, International Journal of Computer Mathematics 81(4) (2004) 483-494.
M.K. Kadalbajoo and K.C. Patidar, Singularly perturbed problems in partial differential equations: a survey, Applied Mathematics and Computation 134(2-3) (2003) 371-429.
M.K. Kadalbajoo and K.C. Patidar, Exponentially fitted spline-in-compression for the numerical solution of singular perturbation problems, Computers and Mathematics with Applications 46(5-6) (2003) 751-767.
M.K. Kadalbajoo and K.C. Patidar, Variable mesh spline-in-compression for the numerical solution of singular perturbation problems, International Journal of Computer Mathematics 80(1) (2003) 83-93.
M.K. Kadalbajoo and K.C. Patidar, Exponentially fitted spline approximation method for solving self-adjoint singular perturbation problems, International Journal of Mathematics and Mathematical Sciences 61 (2003) 3873-3891.
M.K. Kadalbajoo and K.C. Patidar, Spline approximation method for solving self-adjoint singular perturbation problems on non-uniform grids, Journal of Computational Analysis and Applications 5(4) (2003) 425-451.
M.K. Kadalbajoo and K.C. Patidar, Numerical solution of singularly perturbed two-point boundary value problems by spline-in-tension, Applied Mathematics and Computation 131(2-3) (2002) 299-320.
M.K. Kadalbajoo and K.C. Patidar, A survey of numerical techniques for solving singularly perturbed ordinary differential equations, Applied Mathematics and Computation 130(2-3) (2002) 457-510.
M.K. Kadalbajoo and K.C. Patidar, Tension spline for the solution of self-adjoint singular perturbation problems, International Journal of Computer Mathematics 79(7) (2002) 849-865.
M.K. Kadalbajoo and K.C. Patidar, Numerical solution of singularly perturbed non-linear two-point boundary value problems by spline-in-compression, International Journal of Computer Mathematics 79(2) (2002) 271-288.
M.K. Kadalbajoo and K.C. Patidar, Spline techniques for solving singularly perturbed non-linear problems on non-uniform grids, Journal of Optimization Theory and Applications 114(3) (2002) 573-591.
M.K. Kadalbajoo and K.C. Patidar, Spline techniques for the numerical solution of singular perturbation problems, Journal of Optimization Theory and Applications 112(3) (2002) 574-594.
M.K. Kadalbajoo and K.C. Patidar, Tension spline for the numerical solution of singularly perturbed non-linear boundary value problems, Computational and Applied Mathematics 21(3) (2002) 717-742.
M.K. Kadalbajoo and K.C. Patidar, Variable mesh spline approximation method for solving singularly perturbed turning point problems having boundary layer(s), Computers and Mathematics with Application 42(10-11) (2001) 1439-1453.
M.K. Kadalbajoo and K.C. Patidar, Numerical solution of singularly perturbed two-point boundary value problems by spline in compression, International Journal of Computer Mathematics 77(2) (2001) 263-284.
Publications in Conference proceedings:
B.M. Fundzama and K.C. Patidar, Robust numerical method to solve a mathematical model describing Zika virus disease. In T.E. Simos and Ch. Tsitouras (eds.), Proceedings of the International Conference on Numerical Analysis and Applied Mathematics (ICNAAM 2019), published by American Institute of Physics (AIP) Conference Proceedings, Vol. 2293, New York, 2020, pp. 4. DOI: 10.1063/5.0026470. ISBN 978-0-7354-4025-8.
K.C. Patidar and A. Ramanantoanina, Non-standard finite difference method for antagonistic interactions with cross-diffusion. In T.E. Simos and Ch. Tsitouras (eds.), Proceedings of the International Conference on Numerical Analysis and Applied Mathematics (ICNAAM 2018), published by American Institute of Physics (AIP) Conference Proceedings, Vol. 2116, New York, 2019, pp. 4. DOI: 10.1063/1.5044111. ISBN 978-0-7354-1854-7.
E. Pindza, K.C. Patidar and E. Ngounda}, Efficient pricing of European and American options under local volatility. In T.E. Simos and Ch. Tsitouras (eds.), Proceedings of the International Conference on Numerical Analysis and Applied Mathematics (ICNAAM 2017), published by American Institute of Physics (AIP) Conference Proceedings, Vol. 1978, New York, 2018, pp. 4. DOI: 10.1063/1.5044111. ISBN 978-0-7354-1854-7.
A.M.A. Adam, E.B.M. Bashier, M.H.A. Hashim and K.C. Patidar, Fitted Fourier-pseudospectral methods for solving a delayed reaction-diffusion partial differential equation in biology. In T.E. Simos and Ch. Tsitouras (eds.), Proceedings of the International Conference on Numerical Analysis and Applied Mathematics (ICNAAM 2016), published by American Institute of Physics (AIP) Conference Proceedings, Vol. 1863, New York, 2017, pp. 4. DOI: 10.1063/1.4992716. ISBN: 978-0-7354-1538-6.
K.C. Patidar and A.O.M. Sidahmed, Efficient meshfree method for pricing European and American put options on a non-dividend paying asset. In P.N. Agrawal, R.N. Mohapatra, U. Singh and H.M. Srivastava (eds.): Mathematical Analysis and its Applications, Springer Proceedings in Mathematics & Statistics, Vol 143, 2015, pp 443-450. ISSN: 978-81-322-2485-3.
E. Ngounda and K.C. Patidar, A Laplace transform approach for pricing European options. In P.N. Agrawal, R.N. Mohapatra, U. Singh and H.M. Srivastava (eds.): Mathematical Analysis and its Applications, Springer Proceedings in Mathematics & Statistics, Vol 143, 2015, pp 451-461. ISSN: 978-81-322-2485-3.
K.M. Owolabi and K.C. Patidar, Robust numerical simulation of reaction-diffusion models arising in Mathematical Ecology. In G. Akrivis, V. Dougalis, S. Gallopoulos, A. Hadjidimos, I. Kotsireas, C. Makridakis and Y. Saridakis (eds.): Proceedings of NumAn2014 Conference on Numerical Analysis. Recent approaches to Numerical Analysis: Theory, Methods & Applications. Chania, Greece; 2-5 September 2014, pp 222-227. ISBN: 978-960-8475-21-1.
E. Ngounda, K.C. Patidar and E. Pindza, Pricing barrier options using a Laplace transform approach. In A. Adhikari and M.R. Adhikari (eds.): Proceedings of IMBIC (Institute for Mathematics, Bio-informatics, Information-technology and Computer Science), Vol. 2 (2013) (for 7th International Conference of IMBIC on Mathematical Sciences for Advancement of Science and Technology MSAST-2103; Kolkata, India 21-23 December 2013), pp 11-28.
E. Pindza and K.C. Patidar, Spectral method for pricing options in illiquid markets. In T.E. Simos, G. Psihoyios, Ch. Tsitouras and Z. Anastassi (eds.), Numerical Analysis and Applied Mathematics, Proceedings of the International Conference on Numerical Analysis and Applied Mathematics (ICNAAM 2012), published by American Institute of Physics (AIP) Conference Proceedings, Vol. 1479, New York, 2012, pp. 1403-1406.
K.C. Patidar and A.O.M. Sidahmed, An Efficient Meshfree Method for Option Pricing Problems. In T.E. Simos, G. Psihoyios and Ch. Tsitouras (eds.), Numerical Analysis and Applied Mathematics, Proceedings of the International Conference on Numerical Analysis and Applied Mathematics (ICNAAM 2010), published by American Institute of Physics (AIP) Conference Proceedings, Vol. 1281, New York, 2010, pp. 1824-1827.
E.B.M. Bashier and K.C. Patidar, Fitted numerical methods for a system of first order delay differential equations. In: G.S. Ladde, N.G. Medhin, C. Peng and M. Sambandham (eds.), Proceedings of Neural, Parallel & Scientific Computations (4th International Conference on Neural, Parallel & Scientific Computations, Atlanta, Georgia, USA, Aug 11-14, 2010) Dynamic Publishers, Inc., Atlanta, Vol. 4, 2010, pp. 48-53.
J.M.-S. Lubuma and K.C. Patidar, Non-standard finite difference methods for dissipative singular perturbation problems. In: L.J.S. Allen, B. Aulbach, S. Elaydi and R. Sacker (eds.), Difference Equations and Discrete Dynamical Systems, Proceedings of the 9th International Conference on Difference Equations and Applications, University of Southern California, Los Angeles, California, USA, Aug. 2-7, 2004, World Scientific, Singapore, 2005, pp. 185-198.
Extended Abstracts:
P.W.M. Chin, J.M.-S. Lubuma and K.C. Patidar, Regularity and discrete schemes for the heat equation on non-smooth domains. In: TE Simos and G Maroulis (eds.), ICCMSE 2007: Lecture Series on Computation in Modern Science and Engineering 2, 1170-1173, 2007.
J.M.-S. Lubuma and K.C. Patidar, Finite element methods for self-adjoint singular perturbation problems, T.E. Simos and G. Maroulis (eds.), ICCMSE 2005: Advances in Computational Methods in Sciences and Engineering, VSP International Science Publishers, The Netherlands, Lecture Series on Computer and Computational Sciences, 4, 344-347, 2005.
J.M.-S. Lubuma and K.C. Patidar, Non-standard finite difference method for singularly perturbed advection reaction equation. In: T. Simos, G. Psihoyios and Ch. Tsitouras (eds.), ICNAAM, International Conference on Numerical Analysis and Applied Mathematics, 2005, Wiley-VCH Verlag GmBH & Co. KGaA, Weinheim, 354-356, 2005.
J.M.-S. Lubuma and K.C. Patidar, Non-standard finite difference method for self-adjoint singular perturbation problems, T.E. Simos (ed.), Proceedings of the International Conference on Computational Methods in Sciences and Engineering (ICCMSE 2004), VSP International Science Publishers, The Netherlands, Lecture Series on Computer and Computational Sciences, 1, 328-331, 2004.
K.C. Patidar, A numerical study of the dispersion for the two-dimensional Helmholtz equation, G. Psihoyios (ed.), NACoM Extended Abstracts, Proceedings of the International Conference on Numerical Analysis and Computational Mathematics (NACoM 2003), Wiley, 129-130, 2003.
Supervision details:
Ongoing:
4 PhDs: TD Tawe, E Ncube, GAMO Farah, D Elago.
1 MSc: A Rawe.
Completed:
5 Post-Docs (M Akanbi, A Meraj, J Munyakazi, A Ramanantoanina and S Zergani).
22 PhD (18 Main Supervision,3 Co-Supervision): M Dube (2023), EM Adamu (2023), GT Affesa (2023), YA Belay (2023), S Nuugulu (2020), A Shikongo (2020), CK Mbayi (2020) [Co-supervision], MT Sayi (2020) [Co-supervision], W Mergia (2019), KM Owolabi (2014), G Buzuzi (2014), PK Rallabandi (2014), R Malladi (2014), E Ngounda (2012), E Pindza (2012), PWM Chin (2012) [Co-supervision: University of Pretoria], MHM Khabir (2011), AOM Sidahmed (2011), HA Obaid (2011), SMAS Elsheikh (2011), EBM Bashier (2009), JB Munyakazi (2009).
14 MSc: TD Tawe (2022), GAMO Farah (2022), BM Fundzama (2019), FE Kazeem (2015), BG Mvondo (2015), TTA Nyamayaro (2015) [Co-supervision], TPJ Seepi (2014), L Nobaza (2013), D Elago (2011), W Mudzimbabwe (2010) [Co-supervision], G Arotiba (2010), M Londani (2010), A Shikongo (2008), J Wyngaardt (2008).
4 AIMS (African Institute for Mathematical Sciences) MSc mini-theses: GAMO Farah (2016), YA Abdulkadir (2014), AA Aligaz (2014), A Okech (2014).
3 AIMS (African Institute for Mathematical Sciences, Cape Town) Post-grad diploma essays: A Ejugu, B Bello, M Khabir.
10 Accredited 30 credit Honours projects: G Julius, M Tshico, TM Magengenene, KLV Awaseb, NN Moyo, BD Coraizin, MG Constant, O Nkwinika, B Muhire and K Noganta.
Tel: 021 959 3917
Fax:
Email: kpatidar@uwc.ac.za
Biography:
Professor Patidar received his PhD (Mathematics) in 2002 from the Indian Institute of Technology (IIT) Kanpur -- a premier higher educational institute in India. He visited the universities of Tübingen (Germany) and Pretoria (South Africa) for his post-doctoral studies. Subsequently, he joined the University of the Western Cape (South Africa) in 2006 as a senior lecturer and currently holds the position of Senior Professor of Mathematics. He received a C1 rating from the South African National Research Foundation (NRF) for the period 2022-2027. Prior to this, he held a C2 rating for the periods 2010-2015 and 2016-2021. Professor Patidar was the principal investigator for the grants: NRF Focus Area Programme in Mathematics (2007-2008), NRF Competitive Programme for Rated Researchers (2010-2012, 2014-2016, 2017-2019 and 2021-2023) and NRF Programme Knowledge Interchange and Collaboration (2010, 2016).
Professor Patidar’s research involves mathematical methods and scientific computing for application problems that arise from the interactions between natural and life sciences as well as those from the engineering domain. His research involves analytical investigations and numerical experiments using finite difference, finite element, spline approximation and spectral methods for parameter sensitive differential models. He published more than 100 research articles (in journals of international standing), 6 invited book chapters, 12 papers in the proceedings of international conferences and 5 extended abstracts. He graduated 22 PhD and 18 MSc students under his supervision and currently supervising several students. He also acted as an external examiner for PhD theses from local as well as institutions abroad. Some of his accomplished and ongoing well-funded research projects include:
The development of reliable numerical methods for the mathematical models arising in population biology.
The development of efficient numerical methods for option pricing problems in computational finance.
Construction, analysis and implementation of numerical methods for singular perturbation problems.
High order numerical methods for singular perturbation problems.
Administration & Institutional Leadership:
Deputy Dean: Post-Graduate Studies: June 2021 – May 2024.
Acting Deputy Dean: Post-Graduate Studies: Nov 2020 - May 2021.
Head [Department of Mathematics and Applied Mathematics, UWC]: 2018 - 2020; 2021 - 2023.
Member of the Joint Appointments and Promotions Committee of Senate and Council, UWC: 2019, 2021, 2023.
Member of the Management Committee, Faculty of Natural Sciences, UWC: 2018 - 2020, 2021 - 2023.
Deputy Head [Department of Mathematics and Applied Mathematics, UWC]: 2014 - 2017.
Senate Research Committee [Representative from Science Faculty]: July 2013 - Dec 2015.
Senate Scholarships and Fellowships Committee [Representative from Science Faculty]: 2014-2019.
Member of the Executive Team of AIMS (African Institute for Mathematical Sciences) South Africa: 2015-2017; 2018-2020.
Deputy Chair of Science Faculty's Higher Degrees Committee: 2015-2017.
Member of the Executive Committee of Science Faculty's Higher Degrees Committee: 2014-2020.
Member of the Executive Committee of Science Faculty's Post-Graduate Committee: 2011-2013.
Member of Science Faculty's Professorial Appointments/Promotions Committee: 2015- .
Member of the Post-Graduate Committee of the Science Faculty, UWC: 2008-2013.
Member of the Appointment Committee of the Science Faculty, UWC: 2008.
Convener of departmental sub-committees [Library committee 2006-2008; Post-Graduate Studies committee 2008-2013].
Publications:
Summary as of 28 January 2024: Google Scholar Citations: 2439; h-index: 26; i10-index: 62. MathSciNet (Publications: 101; Citations: 453).
Invited book chapters: 6
Research papers in the peer reviewed international journals: 103.
Publications in Conference proceedings: 12
Extended Abstracts: 5.
Further details:
Book Chapters:
E. Ngounda, K.C. Patidar and E. Pindza, Pricing Barrier Options Using Integral Transforms, in B. Toni (ed.), New Trends and Advanced Methods in Interdisciplinary Mathematical Sciences, Springer International Publishing AG, Switzerland, 2017, 221-239.
E.B.M. Bashier and K.C. Patidar, A comparison of numerical methods for systems of first order delay differential equations arising in biology, In: F. Nyabadza, M. Kgosimore and E.M. Lungu (eds.), A Treatise of Biological Models, Nova Science Publishers, Inc., USA, 2012, 75-96.
Application of geometric explicit Runge-Kutta methods to pharmacokinetic models (with M.A. Akanbi), in K.J. Engemann, A.M. Gil-Lafuente and J.M. Merigo (eds.), Modeling and Simulation in Engineering, Economics and Management, Lecture Notes in Business Information Processing, Vol. 115, Springer-Verlag, Berlin, 2012, 259-269.
K.C. Patidar, Numerical methods for multi-parameter singular perturbation problems, in A. Abdulle, J. Banasiak, A. Damlamian and M. Sango (eds.): Multiple Scales Problems in Biomathematics, Mechanics, Physics and Numerics, GAKUTO International Series, Math. Sci. Appl., 31, 327-344, 2009.
J.M.-S. Lubuma and K.C. Patidar, Contributions to the theory of non-standard finite difference methods and applications to singular perturbation problems, Advances in the Applications of Nonstandard Finite Difference Schemes, R.E. Mickens (ed.), World Scientific, Singapore, 2005, 513-560.
A.B. Gumel, K.C. Patidar and R.J. Spiteri, Asymptotically consistent non-standard finite-difference methods for solving mathematical models arising in population biology, Advances in the Applications of Nonstandard Finite Difference Schemes, R.E. Mickens (ed.), World Scientific, Singapore, 2005, 385-421.
Research Papers:
S.M. Nuugulu, F. Gideon and K.C. Patidar, An efficient numerical method for pricing double-barrier
options on an underlying stock governed by a fractal stochastic process, Fractal & Fractional 7 (389) (2023) 15pp. DOI: https://doi.org/10.3390/fractalfract7050389.
C.K. Mbayi, J.B. Munyakazi and K.C. Patidar, A fitted numerical method for interior-layer paraboli convection-diffusion problems, International Journal of Computational Methods 19(10) (2022), Paper no. 2250028, 24 pp.
C.K. Mbayi, J.B. Munyakazi and K.C. Patidar, Layer resolving fitted mesh method for parabolic convection-diffusion problems with a variable diffusion, Journal of Applied Mathematics and Computing, 68 (2022) 1245–1270.
K.M. Owolabi, K.C. Patidar and A. Shikongo, A fitted operator method for a system of delay model of tumor cells dynamics within their micro-environment, Applied Mathematics & Information Sciences, 16 (2) (2022) 367-388.
Kailash C. Patidar and Andriamihaja Ramanantoanina, A non-standard finite difference scheme for a class of predator-prey systems with non-monotonic functional response, Journal of Difference Equations and Applications, 27(9) (2021) 1310-1328.
Elias M. Adamu, Kailash C. Patidar and Andriamihaja Ramanantoanina, An unconditionally stable nonstandard finite difference method to solve a mathematical model describing Visceral Leishmaniasis, Mathematics and Computers in Simulation 187 (2021) 171-190.
S.M. Nuugulu, F. Gideon and K.C. Patidar, A robust numerical scheme for a time fractional Black-Scholes partial differential equation describing stock exchange dynamics, Chaos, Solitons & Fractals 145 (2021) 110753.
S.M. Nuugulu, F. Gideon and K.C. Patidar, A robust numerical solution to a time-fractional Black-Scholes Equation, Advances in Difference Equations 123 (2021), 25pp.
M. Dube and K.C. Patidar, A robust nonstandard finite difference scheme for pricing real estate index options, Journal of Difference Equations and Applications 26 (11-12) (2020) 1471-1493.
W.D. Mergia and K.C. Patidar, High-order semi-implicit linear multistep LG scheme for a three species competition-diffusion system in two-dimensional spatial domain arising in ecology, Communications in Nonlinear Science and Numerical Simulation 84 (2020) 1-16.
C.K. Mbayi, J.B. Munyakazi and K.C. Patidar, A robust fitted numerical method for singularly perturbed turning point problems whose solution exhibits an interior layer, Quaestiones Mathematicae 43(1) (2020) 1-24.
K.M. Owolabi, K.C. Patidar and A. Shikongo, Robust numerical method for a tumor-host model with chemotherapy application, Mathematics in Engineering, Science and Aerospace 11(4) (2020) 739-764.
K.M. Owolabi, K.C. Patidar and A. Shikongo, A fitted operator method for model arising in vascular tumor dynamics, Communications in Mathematical Biology and Neuroscience 2020:4 (2020) 1-21.
K.M. Owolabi, K.C. Patidar and A. Shikongo, Efficient numerical method for a model arising in biological stoichiometry of tumour dynamics, Discrete & Continuous Dynamical Systems - Series S 12(3) (2019) 591-613.
K.M. Owolabi, K.C. Patidar and A. Shikongo, Numerical solution for a problem arising in angiogenic signalling, AIMS Mathematics 4(1) (2019) 43-63.
K.M. Owolabi, K.C. Patidar and A. Shikongo, A fitted numerical method for a model arising in HIV related cancer-immune system dynamics, Communications in Mathematical Biology and Neuroscience 2019 (2019) 1-23.
K.M. Owolabi, K.C. Patidar and A. Shikongo, A fitted operator method for tumor cells dynamics in their micro-environment, Communications in Mathematical Biology and Neuroscience 2019 (2019) 1-44.
J.B. Munyakazi, K.C. Patidar and M.T. Sayi, A fitted numerical method for parabolic turning point singularly perturbed problems with an interior layer, Numerical Methods Partial Differential Equations 35 (6) (2019) 2407-2422.
J.B. Munyakazi, K.C. Patidar and M.T. Sayi, A robust fitted operator finite difference method for singularly perturbed problems whose solution has an interior layer, Mathematics and Computers in Simulation 160 (2019) 155-167.
E. Pindza and K.C. Patidar, A robust spectral method for pricing of American put options on zero-coupon bonds, East Asian Journal on Applied Mathematics 8(1) (2018) 126-138.
W.D. Mergia and K.C. Patidar, Fractional-step $\theta$-method for solving singularly perturbed problem in ecology, Advances in Computational Mathematics 44(3) (2018) 645-671.
K.M. Owolabi, K.C. Patidar and A. Shikongo, Mathematical analysis and numerical simulation of a tumor-host model with chemotherapy application, Communications in Mathematical Biology and Neuroscience 2018 (2018), Article ID 21.
H.A. Obaid, R. Ouifki and K.C. Patidar, A nonstandard finite difference method for solving a mathematical model of HIV-TB co-infection, Journal of Difference Equations and Applications 23(6) (2017) 1105-1132.
E. Pindza, K.M. Owolabi and K.C. Patidar, Barycentric Jacobi spectral method for numerical solutions of the generalized Burgers-Huxley equation, International Journal of Nonlinear Sciences and Numerical Simulation 18(1) (2017) 67-81.
E.B.M. Bashier and K.C. Patidar, Optimal control of an epidemiological model with multiple time delays, Applied Mathematics and Computation 292(1) (2017) 47-56.
K.C. Patidar, Nonstandard finite difference methods: recent trends and further developments, Journal of Difference Equations and Applications 22(6) (2016) 817-849.
W.D. Mergia and K.C. Patidar, Efficient simulation of a slow-fast dynamical system using multirate finite difference schemes, Quaestiones Mathematicae 39(5) (2016) 689-714.
K.C. Patidar, S.K. Datta, T. Biswas and C. Biswas, On comparative growth relationship of iterated entire functions from the view point of slowly changing functions, Facta Universitatis (NIS), Series: Mathematics and Informatics 31(1) (2016) 139-159.
A.M.A. Adam, E.B.M. Bashier, M.H.A. Hashim and K.C. Patidar, Fitted Galerkin spectral method to solve delay partial differential equations, Mathematical Methods in the Applied Sciences 39 (2016) 3102-3115.
G. Buzuzi, J.B. Munyakazi and K.C. Patidar, A fitted numerical method to investigate the effect of various parameters on an MHD flow over an inclined plate, Numerical Methods for Partial Differential Equations 32(1) (2016) 106-120.
K.M. Owolabi and K.C. Patidar, Numerical simulations of multicomponent ecological models with adaptive methods, Theoretical Biology and Medical Modelling 13(1) (2016) 1-25. DOI: 10.1186/s12976-016-0027-4.
K.M. Owolabi and K.C. Patidar, Effect of spatial configuration of an extended nonlinear Kierstead-Slobodkin reaction-transport model with adaptive numerical scheme, SpringerPlus 5(303) (2016) 1-18. DOI: 10.1186/s40064-016-1941-y.
K.M. Owolabi and K.C. Patidar, On the Numerical Exploration of Burgers-Fisher Equation using Robust Implicit-Explicit Schemes, Transylvanian Review 24(6) (2016) 496-508.
K.M. Owolabi and K.C. Patidar, Robust numerical simulation of nonlinear stiff higher-order PDEs, Transylvanian Review 24(6) (2016) 509-526.
H.A. Obaid, R. Ouifki and K.C. Patidar, Analysis of an HIV model with distributed delay and behavior change, International Journal of Bio-mathematics 8(2) (2015). DOI: 10.1142/S1793524515500175.
J.B. Munyakazi and K.C. Patidar, A new fitted operator finite difference method to solve systems of evolutionary reaction-diffusion equations, Quaestiones Mathematicae 38(1) (2015) 121-138.
K.M. Owolabi and K.C. Patidar, Existence and permanence in a diffusive KiSS model with robust numerical simulations, International Journal of Differential Equations 2015, Article ID 485860, 8 pages.
P.K. Rallabandi and K.C. Patidar, A hybrid system of hidden Markov models and recurrent neural networks for learning deterministic finite state automata, International Journal of Computer, Electrical, Automation, Control and Information Engineering 9(11) (2015) 2078-2085.
S. Abbas, D. Bahuguna, E.B.M. Bashier and K.C. Patidar, Pseudo almost periodic mild solutions of quasilinear functional differential equations with application to mathematical biology, Neural, Parallel & Scientific Computations 23 (2015) 318-334.
E. Ngounda and K.C. Patidar, Limitations and improvements of standard spectral methods for pricing standard options, International Journal of Advances in Engineering Sciences and Applied Mathematics 7(3) (2015) 106-113.
E. Pindza, K.C. Patidar and E. Ngounda, Robust spectral method for numerical valuation of European options under Merton's jump-diffusion model, Numerical Methods for Partial Differential Equations 30 (2014) 1169-1188.
S.M.A.S. Elsheikh, K.C. Patidar and R. Ouifki, Analysis of a Malaria model with a distributed delay, IMA Journal of Applied Mathematics 79(6) (2014) 1139-1160.
S.M.A.S. Elsheikh, R. Ouifki and K.C. Patidar, A nonstandard finite difference method to solve a model of HIV-Malaria co-infection, Journal of Difference Equations and Applications 20(3) (2014) 354-378.
E. Ngounda, K.C. Patidar and E. Pindza, A robust spectral method for solving Heston's model, Journal of Optimization Theory and Applications 161(1) (2014) 164-178.
K.M. Owolabi and K.C. Patidar, Higher-order time-stepping methods for time-dependent reaction-diffusion equations arising in biology, Applied Mathematics and Computation 240(1) (2014) 30-50.
K.M. Owolabi and K.C. Patidar, Numerical solution of singular patterns in one-dimensional Gray-Scott-like models, International Journal of Nonlinear Sciences and Numerical Simulation 15(7-8) (2014) 437-462.
J.B. Munyakazi and K.C. Patidar, Performance of Richardson extrapolation on some numerical methods for a singularly perturbed turning point problem whose solution has boundary layers, Journal of the Korean Mathematical Society 51(4) (2014) 679-702.
M.H.M. Khabir and K.C. Patidar, Comparison of some numerical methods for option pricing problems, Neural, Parallel, and Scientific Computations 22 (2014) 521-538.
E. Pindza, K.C. Patidar and E. Ngounda, Implicit-explicit predictor-corrector methods combined with improved spectral methods for pricing European style vanilla and exotic options, Electronic Transactions on Numerical Analysis 40 (2013) 268-293.
E. Ngounda, K.C. Patidar and E. Pindza, Contour integral method for European options with jumps, Communications in Nonlinear Science and Numerical Simulation 18 (2013) 478-492.
E. Pindza and K.C. Patidar, A comparative performance of exponential time differencing and implicit explicit methods for pricing European options under the Black-Scholes and Merton jump-diffusion models, Review of the Bulletin of Calcutta Mathematical Society 21(1) (2013) 51-70.
H.A. Obaid, R. Ouifki and K.C. Patidar, An unconditionally stable nonstandard finite difference methods applied to a mathematical model of HIV infection, International Journal of Applied Mathematics and Computer Science 23(2) (2013) 357-372.
E.B.M. Bashier and K.C. Patidar, An efficient fitted operator method to solve delayed singularly perturbed differential-difference equations, Neural, Parallel & Scientific Computations 21 (2013) 217-234.
K.K. Sharma, P. Rai and K.C. Patidar, A review on singularly perturbed differential equations with turning points and interior layers, Applied Mathematics and Computation 219(22) (2013) 10575-10609.
J.B. Munyakazi and K.C. Patidar, A fitted numerical method for singularly perturbed parabolic reaction-diffusion problems, Computational and Applied Mathematics 32 (2013) 509-519.
MHM Khabir and KC Patidar, Spline approximation method to solve an option pricing problem, Journal of Difference Equations and Applications, 18(11) (2012) 1801-1816.
W. Mudzimbabwe, K.C. Patidar and P.J. Witbooi, European basket option pricing by maximizing over a subset of lower bounds, Quaestiones Mathematicae 35(2) (2012) 507-520.
JB Munyakazi and KC Patidar, Novel fitted operator finite difference methods for singularly perturbed elliptic convection-diffusion problems in two dimensions, Journal of Difference Equations and Applications, 18(5) (2012) 799-813.
W Mudzimbabwe, KC Patidar and PJ Witbooi, A reliable numerical method to price arithmetic Asian options, Applied Mathematics and Computation, 218(22) (2012), 10934-10942.
JB Munyakazi and KC Patidar, An efficient numerical method for a system of singularly perturbed reaction-diffusion equations, Neural, Parallel & Scientific Computations 20 (2012) 173-190.
I Ahmed I, PJ Witbooi and KC Patidar, Modeling the dynamics of an epidemic under vaccination in two interacting populations, Journal of Applied Mathematics, Published online. 14 pages. DOI:10.1155/2012/275902.
E.B.M. Bashier and K.C. Patidar, A fitted numerical method for a system of partial delay differential equations, Computers and Mathematics with Applications 61(6) (2011) 1475-1492.
E.B.M. Bashier and K.C. Patidar, A novel fitted operator finite difference method for a singularly perturbed delay parabolic partial differential equation, Applied Mathematics and Computation 217 (2011) 4728-4739.
E.B.M. Bashier and K.C. Patidar, A second order fitted operator finite difference method for a singularly perturbed delay parabolic partial differential equation, Journal of Difference Equations and Applications 17(5) (2011) 779-794.
K.C. Patidar, A new class of finite element method for convection-diffusion-reaction problems, Neural, Parallel & Scientific Computations 18(2) (2010) 237-252.
E.B.M. Bashier and K.C. Patidar, An almost second order fitted mesh numerical method for a singularly perturbed delay parabolic partial differential equation, Neural, Parallel & Scientific Computations 18(2) (2010) 137-154.
M.K. Kadalbajoo and K.C. Patidar, Variable mesh spline approximation method for solving singularly perturbed turning point problems having interior layer, Neural, Parallel & Scientific Computations 18(2) (2010) 207-220.
J.B. Munyakazi and K.C. Patidar, Higher order numerical methods for singularly perturbed elliptic problems, Neural, Parallel & Scientific Computations 18(1) (2010) 75-88.
J.B. Munyakazi and K.C. Patidar, Limitations of Richardson's extrapolation for a high order fitted mesh method for self-adjoint singularly perturbed problems, Journal of Applied Mathematics and Computing 32(1) (2010) 219-236.
J.M.-S. Lubuma and K.C. Patidar, Reliable finite element methods for self-adjoint singular perturbation problems, Quaestiones Mathematicae, 32(3) (2009) 397-413.
J.M.-S. Lubuma and K.C. Patidar, Towards the implementation of the singular function method for singular perturbation problems, Applied Mathematics and Computations 209 (1) (2009) 68-74.
K.C. Patidar, A robust fitted operator finite difference method for a two-parameter singular perturbation problem, Journal of Difference Equations and Applications 14 (12) (2008) 1197-1214.
J.B. Munyakazi and K.C. Patidar, On Richardson extrapolation for fitted operator finite difference methods, Applied Mathematics and Computations 201(1-2) (2008) 465-480.
C. Le Roux and K.C. Patidar, On the flow of a generalized Burgers fluid in an orthogonal rheometer, Nonlinear Analysis Series B: Real World Applications 9(5) (2008) 1882-1893.
S. Abelman and K.C. Patidar, Comparison of some recent numerical methods for initial value problems for stiff ordinary differential equations, Computers and Mathematics with Applications 55(4) (2008) 733-744.
K.C. Patidar, High order parameter uniform numerical method for singular perturbation problems, Applied Mathematics and Computation 188 (2007) 720-733.
K.C. Patidar and A. Shikongo, The applications of asymptotic analysis for developing reliable numerical method for a model singular perturbation problem, Journal of Numerical Analysis Industrial and Applied Mathematics 2(3-4) (2007) 193-207.
J.M.-S. Lubuma and K.C. Patidar, Solving singularly perturbed advection reaction equation via non-standard finite difference methods, Mathematical Methods in the Applied Sciences 30(14) (2007) 1627-1637.
J.M.-S. Lubuma and K.C. Patidar, $\varepsilon$-uniform non-standard finite difference methods for singularly perturbed nonlinear boundary value problems, Advances in Mathematical Sciences and Applications 17(2) (2007) 651-665.
J.M.-S. Lubuma and K.C. Patidar, Non-standard methods for singularly perturbed problems possessing oscillatory/layer solutions, Applied Mathematics and Computation 187 (2007) 1147-1160.
K.C. Patidar and K. K. Sharma, Uniformly convergent nonstandard finite difference methods for singularly perturbed differential difference equations with delay and advance, International Journal for Numerical Methods in Engineering 66 (2006) 272-296.
M.K. Kadalbajoo, K.C. Patidar and K. K. Sharma, $\varepsilon$-uniformly convergent fitted methods for the numerical solution of the problems arising from singularly perturbed general DDEs, Applied Mathematics and Computation 182 (2006) 119-139.
J.M.-S. Lubuma and K.C. Patidar, Uniformly convergent non-standard finite difference methods for self-adjoint singular perturbation problems, Journal of Computational and Applied Mathematics 191 (2006) 229-238.
K.C. Patidar and K. K. Sharma, $\varepsilon$-uniformly convergent non-standard finite difference methods for singularly perturbed differential difference equations with small delay, Applied Mathematics and Computation 175 (2006) 864-890.
M.K. Kadalbajoo and K.C. Patidar, $\varepsilon$-uniformly convergent fitted mesh finite difference methods for general singular perturbation problems, Applied Mathematics and Computation 179 (2006) 248-266.
K.C. Patidar, On the use of non-standard finite difference methods, Journal of Difference Equations and Applications 11 (2005) 735-758.
K.C. Patidar, High order fitted operator numerical method for the self-adjoint singular perturbation problems, Applied Mathematics and Computation 171(1) (2005) 547-566.
K.C. Patidar, Dispersion induced by the pollution for the wave equation, Applied Mathematics and Computation 160 (2005) 329-341.
K.C. Patidar, Pollution free discretization of the wave equation, International Journal of Computer Mathematics 81(4) (2004) 483-494.
M.K. Kadalbajoo and K.C. Patidar, Singularly perturbed problems in partial differential equations: a survey, Applied Mathematics and Computation 134(2-3) (2003) 371-429.
M.K. Kadalbajoo and K.C. Patidar, Exponentially fitted spline-in-compression for the numerical solution of singular perturbation problems, Computers and Mathematics with Applications 46(5-6) (2003) 751-767.
M.K. Kadalbajoo and K.C. Patidar, Variable mesh spline-in-compression for the numerical solution of singular perturbation problems, International Journal of Computer Mathematics 80(1) (2003) 83-93.
M.K. Kadalbajoo and K.C. Patidar, Exponentially fitted spline approximation method for solving self-adjoint singular perturbation problems, International Journal of Mathematics and Mathematical Sciences 61 (2003) 3873-3891.
M.K. Kadalbajoo and K.C. Patidar, Spline approximation method for solving self-adjoint singular perturbation problems on non-uniform grids, Journal of Computational Analysis and Applications 5(4) (2003) 425-451.
M.K. Kadalbajoo and K.C. Patidar, Numerical solution of singularly perturbed two-point boundary value problems by spline-in-tension, Applied Mathematics and Computation 131(2-3) (2002) 299-320.
M.K. Kadalbajoo and K.C. Patidar, A survey of numerical techniques for solving singularly perturbed ordinary differential equations, Applied Mathematics and Computation 130(2-3) (2002) 457-510.
M.K. Kadalbajoo and K.C. Patidar, Tension spline for the solution of self-adjoint singular perturbation problems, International Journal of Computer Mathematics 79(7) (2002) 849-865.
M.K. Kadalbajoo and K.C. Patidar, Numerical solution of singularly perturbed non-linear two-point boundary value problems by spline-in-compression, International Journal of Computer Mathematics 79(2) (2002) 271-288.
M.K. Kadalbajoo and K.C. Patidar, Spline techniques for solving singularly perturbed non-linear problems on non-uniform grids, Journal of Optimization Theory and Applications 114(3) (2002) 573-591.
M.K. Kadalbajoo and K.C. Patidar, Spline techniques for the numerical solution of singular perturbation problems, Journal of Optimization Theory and Applications 112(3) (2002) 574-594.
M.K. Kadalbajoo and K.C. Patidar, Tension spline for the numerical solution of singularly perturbed non-linear boundary value problems, Computational and Applied Mathematics 21(3) (2002) 717-742.
M.K. Kadalbajoo and K.C. Patidar, Variable mesh spline approximation method for solving singularly perturbed turning point problems having boundary layer(s), Computers and Mathematics with Application 42(10-11) (2001) 1439-1453.
M.K. Kadalbajoo and K.C. Patidar, Numerical solution of singularly perturbed two-point boundary value problems by spline in compression, International Journal of Computer Mathematics 77(2) (2001) 263-284.
Publications in Conference proceedings:
B.M. Fundzama and K.C. Patidar, Robust numerical method to solve a mathematical model describing Zika virus disease. In T.E. Simos and Ch. Tsitouras (eds.), Proceedings of the International Conference on Numerical Analysis and Applied Mathematics (ICNAAM 2019), published by American Institute of Physics (AIP) Conference Proceedings, Vol. 2293, New York, 2020, pp. 4. DOI: 10.1063/5.0026470. ISBN 978-0-7354-4025-8.
K.C. Patidar and A. Ramanantoanina, Non-standard finite difference method for antagonistic interactions with cross-diffusion. In T.E. Simos and Ch. Tsitouras (eds.), Proceedings of the International Conference on Numerical Analysis and Applied Mathematics (ICNAAM 2018), published by American Institute of Physics (AIP) Conference Proceedings, Vol. 2116, New York, 2019, pp. 4. DOI: 10.1063/1.5044111. ISBN 978-0-7354-1854-7.
E. Pindza, K.C. Patidar and E. Ngounda}, Efficient pricing of European and American options under local volatility. In T.E. Simos and Ch. Tsitouras (eds.), Proceedings of the International Conference on Numerical Analysis and Applied Mathematics (ICNAAM 2017), published by American Institute of Physics (AIP) Conference Proceedings, Vol. 1978, New York, 2018, pp. 4. DOI: 10.1063/1.5044111. ISBN 978-0-7354-1854-7.
A.M.A. Adam, E.B.M. Bashier, M.H.A. Hashim and K.C. Patidar, Fitted Fourier-pseudospectral methods for solving a delayed reaction-diffusion partial differential equation in biology. In T.E. Simos and Ch. Tsitouras (eds.), Proceedings of the International Conference on Numerical Analysis and Applied Mathematics (ICNAAM 2016), published by American Institute of Physics (AIP) Conference Proceedings, Vol. 1863, New York, 2017, pp. 4. DOI: 10.1063/1.4992716. ISBN: 978-0-7354-1538-6.
K.C. Patidar and A.O.M. Sidahmed, Efficient meshfree method for pricing European and American put options on a non-dividend paying asset. In P.N. Agrawal, R.N. Mohapatra, U. Singh and H.M. Srivastava (eds.): Mathematical Analysis and its Applications, Springer Proceedings in Mathematics & Statistics, Vol 143, 2015, pp 443-450. ISSN: 978-81-322-2485-3.
E. Ngounda and K.C. Patidar, A Laplace transform approach for pricing European options. In P.N. Agrawal, R.N. Mohapatra, U. Singh and H.M. Srivastava (eds.): Mathematical Analysis and its Applications, Springer Proceedings in Mathematics & Statistics, Vol 143, 2015, pp 451-461. ISSN: 978-81-322-2485-3.
K.M. Owolabi and K.C. Patidar, Robust numerical simulation of reaction-diffusion models arising in Mathematical Ecology. In G. Akrivis, V. Dougalis, S. Gallopoulos, A. Hadjidimos, I. Kotsireas, C. Makridakis and Y. Saridakis (eds.): Proceedings of NumAn2014 Conference on Numerical Analysis. Recent approaches to Numerical Analysis: Theory, Methods & Applications. Chania, Greece; 2-5 September 2014, pp 222-227. ISBN: 978-960-8475-21-1.
E. Ngounda, K.C. Patidar and E. Pindza, Pricing barrier options using a Laplace transform approach. In A. Adhikari and M.R. Adhikari (eds.): Proceedings of IMBIC (Institute for Mathematics, Bio-informatics, Information-technology and Computer Science), Vol. 2 (2013) (for 7th International Conference of IMBIC on Mathematical Sciences for Advancement of Science and Technology MSAST-2103; Kolkata, India 21-23 December 2013), pp 11-28.
E. Pindza and K.C. Patidar, Spectral method for pricing options in illiquid markets. In T.E. Simos, G. Psihoyios, Ch. Tsitouras and Z. Anastassi (eds.), Numerical Analysis and Applied Mathematics, Proceedings of the International Conference on Numerical Analysis and Applied Mathematics (ICNAAM 2012), published by American Institute of Physics (AIP) Conference Proceedings, Vol. 1479, New York, 2012, pp. 1403-1406.
K.C. Patidar and A.O.M. Sidahmed, An Efficient Meshfree Method for Option Pricing Problems. In T.E. Simos, G. Psihoyios and Ch. Tsitouras (eds.), Numerical Analysis and Applied Mathematics, Proceedings of the International Conference on Numerical Analysis and Applied Mathematics (ICNAAM 2010), published by American Institute of Physics (AIP) Conference Proceedings, Vol. 1281, New York, 2010, pp. 1824-1827.
E.B.M. Bashier and K.C. Patidar, Fitted numerical methods for a system of first order delay differential equations. In: G.S. Ladde, N.G. Medhin, C. Peng and M. Sambandham (eds.), Proceedings of Neural, Parallel & Scientific Computations (4th International Conference on Neural, Parallel & Scientific Computations, Atlanta, Georgia, USA, Aug 11-14, 2010) Dynamic Publishers, Inc., Atlanta, Vol. 4, 2010, pp. 48-53.
J.M.-S. Lubuma and K.C. Patidar, Non-standard finite difference methods for dissipative singular perturbation problems. In: L.J.S. Allen, B. Aulbach, S. Elaydi and R. Sacker (eds.), Difference Equations and Discrete Dynamical Systems, Proceedings of the 9th International Conference on Difference Equations and Applications, University of Southern California, Los Angeles, California, USA, Aug. 2-7, 2004, World Scientific, Singapore, 2005, pp. 185-198.
Extended Abstracts:
P.W.M. Chin, J.M.-S. Lubuma and K.C. Patidar, Regularity and discrete schemes for the heat equation on non-smooth domains. In: TE Simos and G Maroulis (eds.), ICCMSE 2007: Lecture Series on Computation in Modern Science and Engineering 2, 1170-1173, 2007.
J.M.-S. Lubuma and K.C. Patidar, Finite element methods for self-adjoint singular perturbation problems, T.E. Simos and G. Maroulis (eds.), ICCMSE 2005: Advances in Computational Methods in Sciences and Engineering, VSP International Science Publishers, The Netherlands, Lecture Series on Computer and Computational Sciences, 4, 344-347, 2005.
J.M.-S. Lubuma and K.C. Patidar, Non-standard finite difference method for singularly perturbed advection reaction equation. In: T. Simos, G. Psihoyios and Ch. Tsitouras (eds.), ICNAAM, International Conference on Numerical Analysis and Applied Mathematics, 2005, Wiley-VCH Verlag GmBH & Co. KGaA, Weinheim, 354-356, 2005.
J.M.-S. Lubuma and K.C. Patidar, Non-standard finite difference method for self-adjoint singular perturbation problems, T.E. Simos (ed.), Proceedings of the International Conference on Computational Methods in Sciences and Engineering (ICCMSE 2004), VSP International Science Publishers, The Netherlands, Lecture Series on Computer and Computational Sciences, 1, 328-331, 2004.
K.C. Patidar, A numerical study of the dispersion for the two-dimensional Helmholtz equation, G. Psihoyios (ed.), NACoM Extended Abstracts, Proceedings of the International Conference on Numerical Analysis and Computational Mathematics (NACoM 2003), Wiley, 129-130, 2003.
Supervision details:
Ongoing:
4 PhDs: TD Tawe, E Ncube, GAMO Farah, D Elago.
1 MSc: A Rawe.
Completed:
5 Post-Docs (M Akanbi, A Meraj, J Munyakazi, A Ramanantoanina and S Zergani).
22 PhD (18 Main Supervision,3 Co-Supervision): M Dube (2023), EM Adamu (2023), GT Affesa (2023), YA Belay (2023), S Nuugulu (2020), A Shikongo (2020), CK Mbayi (2020) [Co-supervision], MT Sayi (2020) [Co-supervision], W Mergia (2019), KM Owolabi (2014), G Buzuzi (2014), PK Rallabandi (2014), R Malladi (2014), E Ngounda (2012), E Pindza (2012), PWM Chin (2012) [Co-supervision: University of Pretoria], MHM Khabir (2011), AOM Sidahmed (2011), HA Obaid (2011), SMAS Elsheikh (2011), EBM Bashier (2009), JB Munyakazi (2009).
14 MSc: TD Tawe (2022), GAMO Farah (2022), BM Fundzama (2019), FE Kazeem (2015), BG Mvondo (2015), TTA Nyamayaro (2015) [Co-supervision], TPJ Seepi (2014), L Nobaza (2013), D Elago (2011), W Mudzimbabwe (2010) [Co-supervision], G Arotiba (2010), M Londani (2010), A Shikongo (2008), J Wyngaardt (2008).
4 AIMS (African Institute for Mathematical Sciences) MSc mini-theses: GAMO Farah (2016), YA Abdulkadir (2014), AA Aligaz (2014), A Okech (2014).
3 AIMS (African Institute for Mathematical Sciences, Cape Town) Post-grad diploma essays: A Ejugu, B Bello, M Khabir.
10 Accredited 30 credit Honours projects: G Julius, M Tshico, TM Magengenene, KLV Awaseb, NN Moyo, BD Coraizin, MG Constant, O Nkwinika, B Muhire and K Noganta.
Position: Professor
Tel: +27 (021) 959 3021
Fax: +27 (021) 959 1241
Email: emwambene@uwc.ac.za
He has published and supervised postgraduate students in algebraic graph theory, coding theory, and the application of graph theory to bioinformatics.
Tel: +27 (021) 959 3021
Fax: +27 (021) 959 1241
Email: emwambene@uwc.ac.za
Bio:
Eric Mwambene has a doctorate in algebraic combinatorics from University of Vienna, an MSc in discrete mathematics from UZ, and an MSc in Artificial Intelligence from Imperial College, London.He has published and supervised postgraduate students in algebraic graph theory, coding theory, and the application of graph theory to bioinformatics.
Position: Associate Professor
Tel: +27 (021) 959 2270
Fax: +27 (021) 959 1241
Office: 1.50
Email: emehdinezhad@uwc.ac.za
Tel: +27 (021) 959 2270
Fax: +27 (021) 959 1241
Office: 1.50
Email: emehdinezhad@uwc.ac.za
Position: Professor
Rao Appadu graduated with a PhD in Computational Fluid Dynamics in April 2010. He then did a postdoc at University of Cape Town from July 2010 to June 2011. He worked in the department of Mathematics and Applied Mathematics at institutions such as University of Pretoria and Nelson Mandela University (NMU) before joining University of Western Cape. He got opportunity to supervise 4 PhD students and they graduated in 2017 (2), 2020 and 2023. He also guided 2 postdoc fellows in March 2021 to September 2022 and March 2020 to February 2024 respectively.
Publication details as at October 2025:
1.Google Scholar
Citations:801, h-index: 15
2. Scopus
Publications: 48 journals,15 conference proceedings and 2 book chapters, citations: 546
Research awards
Current Research interests
Bio:
Rao Appadu is a Professor in the department of Mathematics and Applied Mathematics. He currently teaches at undergraduate level and also supervises MSc and PhD students in the fields of numerical analysis and mathematical biology. He currently has an NRF rating in C2 category (January 2021 to December 2026). He also has experience as referee of some international journals, topic and review editor for Frontiers in Applied Mathematics and Statistics and is currently a guest editor for Advances in Differential Equations and Control Processes.Rao Appadu graduated with a PhD in Computational Fluid Dynamics in April 2010. He then did a postdoc at University of Cape Town from July 2010 to June 2011. He worked in the department of Mathematics and Applied Mathematics at institutions such as University of Pretoria and Nelson Mandela University (NMU) before joining University of Western Cape. He got opportunity to supervise 4 PhD students and they graduated in 2017 (2), 2020 and 2023. He also guided 2 postdoc fellows in March 2021 to September 2022 and March 2020 to February 2024 respectively.
Publication details as at October 2025:
1.Google Scholar
Citations:801, h-index: 15
2. Scopus
Publications: 48 journals,15 conference proceedings and 2 book chapters, citations: 546
Research awards
- Emerging Researcher of the year award for Faculty of Science awarded on 27 November 2023 at NMU.
- Research Excellence Award obtained on 24 October 2024 at NMU.
Current Research interests
- Numerical Analysis (Construction and Analysis of some finite difference methods for some (fractional) partial differential equations with applications in mathematical biology, mathematical physics).
- Mathematical biology (Qualitative analysis of some models for coral reefs formation and predator prey models).
- Numerical Optimisation.
Position: Lecturer
Tel: +27 (021) 959 3018
Tel: +27 (021) 959 3018
Bio:
Currently a lecturer at the department of Mathematics and Applied Mathematics. Main research interest lies between Category Theory and General Topology.Position: Senior Lecturer
Tel: +27 (021) 959 3025
Fax: +27 (021) 959 1241
Tel: +27 (021) 959 3025
Fax: +27 (021) 959 1241
Bio:
Dr. C. Makasu is a graduate of the University of Zimbabwe. His area of specialization is stochastic analysis, with applications in mathematical finance. From 2003 to 2005, he was a postdoc fellow at the Mathematics Institute, University of Oslo, Norway. Dr. Makasu has taught in various Universities and joined the Department of Mathematics and Applied Mathematics (UWC) in February, 2010. He has published in various international journals and has also served as a reviewer for the Asian journal of Control, IEEE Transactions on Automatic control, Optimization, Systems and Control Letters, and the International journal of Systems Science.Position: ECP lecturer
Tel: +27 (021) 959 3017
Fax: +27 (021) 959 1241
Tel: +27 (021) 959 3017
Fax: +27 (021) 959 1241
Bio:
Mr. G. van Schalkwyk is currently a PhD candidate in the Department of Mathematics and Applied Mathematics at the University of the Western Cape. His research interests include risk management, financial engineering and optimal control.Position: Lecturer
Tel: +27 (021) 959 9762
Fax: +27 (021) 959 1241
Tel: +27 (021) 959 9762
Fax: +27 (021) 959 1241
Bio:
Grant Muller is a lecturer in the Department of Mathematics and Applied Mathematics at the University of the Western Cape (UWC). He obtained his Ph.D. degree in applied mathematics from UWC in 2015. Grant’s research interests include the application of optimal control theory and mathematical modelling in finance and epidemiology.Position: ECP Lecturer
Tel: +27 (021) 959 9762
Fax: +27 (021) 959 1241
Tel: +27 (021) 959 9762
Fax: +27 (021) 959 1241
Bio:
Mr Mozart is currently a PhD student in the Department of Mathematics and Applied Mathematics of the University of the Western Cape. His doctoral research is in epidemiology and the stochastic control and mathematical modelling of the spread of the HIV/AIDS epidemic in South Africa. Mr Mozart has been employed as ECP Lecturer since 2011.Position: Lecturer
Tel: +27 (021) 959 2055
Fax: +27 (021) 959 1241
Tel: +27 (021) 959 2055
Fax: +27 (021) 959 1241
Bio:
Sibaliwe Maku Vyambwera completed her degree B.Sc. (Computer Science) at the University of Transkei (Walter Sisulu University). She completed her B.Sc Honours and MSc at the University of Western Cape. Her research field focuses on mathematical modelling in epidemiology using both deterministic and stochastic differential equations.Position: Senior Lecturer
The abstract work of the PhD was applied to stochastic processes (Claude Leon Postdoctoral supervision of Professor Banasiak) in the form of implicit Fokker Planck equations associated with the extended Chapman-Kolmogorov equation and a non-commutative extension of the Feller convolution for multi-dimensional probability distributions. The semigroup solution to the state-space equation of control systems (infinite-dimensional) was extended to ill-posed systems (NWU Postdoctoral supervision of Professor Ter Horst)
He received a C2 rating (established researcher) from the South African National Research Foundation (NRF) in 2022.
Bio:
Evolution equations is an operator theoretic approach that reduces a partial differential equation into a simpler ordinary differential equation (in an infinite dimensional space). The operator theoretic approach of empathy theory (pioneered by Professor Niko Sauer), in contrast to the well known Semigroup theory, uses a double family of evolution operators. For the corresponding pair of intertwined resolvent operators, Hille-Yosida results was established by Banach algebra techniques. The new paradigm shift of generalized operators was also introduced in the PhD.The abstract work of the PhD was applied to stochastic processes (Claude Leon Postdoctoral supervision of Professor Banasiak) in the form of implicit Fokker Planck equations associated with the extended Chapman-Kolmogorov equation and a non-commutative extension of the Feller convolution for multi-dimensional probability distributions. The semigroup solution to the state-space equation of control systems (infinite-dimensional) was extended to ill-posed systems (NWU Postdoctoral supervision of Professor Ter Horst)
He received a C2 rating (established researcher) from the South African National Research Foundation (NRF) in 2022.
Position: ECP Lecturer
Tel: +27 084 066 0541
Fax: +27 (021) 959 1241
Tel: +27 084 066 0541
Fax: +27 (021) 959 1241
Bio:
Marshall Ongansie is a MSc student in Computational Finance at the University of the Western Cape. Before enrolling for his MSc, he completed his BSc and BSc (Hons) degrees at the University of the Western Cape. His research field is mathematical modelling Epidemiology. Marshall is currently lecturing first year calculus infused with pre-calculus under the Extended Curriculum Program at the University of the Western Cape.Current/Previous Extraordinary and Honorary Professor
Position: Extraordinary Professor
2. Postdoc in Topology at Universita' degli Studi di Palermo in 2010 (Italy).
3. Postdoc in Dynamical Systems at Universita' degli Studi di Palermo in 2012 (Italy).
4. Postdoc in Geometry Group Theory at Instituto de Matematica Pura e Aplicada of Rio de Janeiro (Brazil) in 2013.
5. Senior Lecturer at University of Cape Town (South Africa) in 2014-2024.
6. Associate Professor at University of Camerino (Italy) since 2024.
Biography
1. PhD in Mathematics at Universita' degli Studi di Napoli Federico II in 2009 (Italy).2. Postdoc in Topology at Universita' degli Studi di Palermo in 2010 (Italy).
3. Postdoc in Dynamical Systems at Universita' degli Studi di Palermo in 2012 (Italy).
4. Postdoc in Geometry Group Theory at Instituto de Matematica Pura e Aplicada of Rio de Janeiro (Brazil) in 2013.
5. Senior Lecturer at University of Cape Town (South Africa) in 2014-2024.
6. Associate Professor at University of Camerino (Italy) since 2024.
Position: Extraordinary Professor
Tel: +27 (021) 959 3019
Tel: +27 (021) 959 3019
1. Head of Department of Pure and Applied Mathematics - University of the Western Cape. 1995 - 1996. 2. Dean of Faculty of Natural Sciences - University of the Western Cape. 1999 - 2000. 3. Deputy Vice-Chancellor(Research) - University of the Witwatersrand. 2000 - 2003. 4. Vice-Chancellor and Principal - University of the Witwatersrand. 2003 - 2013.
Position: Emeritus Professor
Tel: +27 (021) 959 3019
Fax: +27 (021) 959 1241
Tel: +27 (021) 959 3019
Fax: +27 (021) 959 1241
Bio:
I have been in my current post as lecturer for the past 35 years. I have taught all undergraduate courses offered by our department. At the postgraduate level I have taught courses in Group Theory, Rings and Modules, Near-rings, Representation Theory , Set Theory and Logic and Coding Theory. I have supervised Honours Projects, MSc (both in mathematics and mathematics education) and PhD students. I serve as external examiner for many universities for undergraduate as well as postgraduate courses and for masters and PhD theses.Administrative and Professional support
Position: Senior Officer
Tel: +27 (021) 950 3015
Fax: +27 (021) 950 1241
Employment: At the beginning of the year 2012 (February 2012 - April 2012), she was employed as a tutor at UCT. She held the position of full tutor for the first year Mathematics ADP (Academic Development Program) course in Science (MAM 1005H and MAM 1006H) at UCT. This position allowed her to gain experience in developing skilled teaching techniques, since these courses caters for students of disadvantage backgrounds. She also, attended a week long tutor workshop given by the Numeracy Centre of UCT. Currently (from the 2 May 2012 - to Date), Leila is employed by the University of Western Cape (UWC) as a Senior Officer in the Department of Mathematics and Applied Mathematics. Her job description entails: To provide academic assistance towards the first year mainstream calculus mathematics course (MAT 105) in terms of; management and co-ordination of tutorial sessions, administration of tutors during the tutorial sessions, provide extra consultation sessions to students, marking of examinations, class tests and tutorial test. This position has allowed her to gain valuable experience in mathematics education at a tertiary level as well as helped her improve her administration and management skills needed for convening a mathematics course at a tertiary institute.
Studying and Research Interests: Her future intensions are to further her studies at Phd level and her research interests are as follows; Computational Electromagnetics (CEM), with particular interest in the Finite Element Method (FEM) and Vector Finite Elements, Electromagnetic Field Theory and Advanced Vector Calculus, Mathematics education at a tertiary level.
Hobbies: Leila enjoys the following hobbies which help her relax and provides a balance in her life; Tai-Chi, hiking and vegetable gardening.
Tel: +27 (021) 950 3015
Fax: +27 (021) 950 1241
Bio:
Leila attended Islamia College which is situated in Lansdowne, Cape Town and in 1999, she received her Senior Certificate. In 2005, she graduated with a BSc in Applied Mathematics from the University of Cape Town (UCT) and in 2006, she graduated with a BSc (Honours) in Material Science from UCT. The title of her honours major project was; Modelling the Mechanical Properties of Polymer-Matrix Composites and Polymers. After her honours graduation, she also received the 4th Year Material Science Class Medal which was awarded on Academic Merit for attaining first position in class. In 2011, she then graduated with an MSc in Engineering (Electrical) at the UCT. It was the first time that a Computational Electromagnetics (CEM) project using vector finite elements was attempted at UCT. The title of her Dissertation was; The Finite Element Method using Vector Finite Elements Applied to Eddy Current Problems.Employment: At the beginning of the year 2012 (February 2012 - April 2012), she was employed as a tutor at UCT. She held the position of full tutor for the first year Mathematics ADP (Academic Development Program) course in Science (MAM 1005H and MAM 1006H) at UCT. This position allowed her to gain experience in developing skilled teaching techniques, since these courses caters for students of disadvantage backgrounds. She also, attended a week long tutor workshop given by the Numeracy Centre of UCT. Currently (from the 2 May 2012 - to Date), Leila is employed by the University of Western Cape (UWC) as a Senior Officer in the Department of Mathematics and Applied Mathematics. Her job description entails: To provide academic assistance towards the first year mainstream calculus mathematics course (MAT 105) in terms of; management and co-ordination of tutorial sessions, administration of tutors during the tutorial sessions, provide extra consultation sessions to students, marking of examinations, class tests and tutorial test. This position has allowed her to gain valuable experience in mathematics education at a tertiary level as well as helped her improve her administration and management skills needed for convening a mathematics course at a tertiary institute.
Studying and Research Interests: Her future intensions are to further her studies at Phd level and her research interests are as follows; Computational Electromagnetics (CEM), with particular interest in the Finite Element Method (FEM) and Vector Finite Elements, Electromagnetic Field Theory and Advanced Vector Calculus, Mathematics education at a tertiary level.
Hobbies: Leila enjoys the following hobbies which help her relax and provides a balance in her life; Tai-Chi, hiking and vegetable gardening.
