Position: | Senior Professor & Head of Department |

Department: | Department of Mathematics |

Faculty: | Faculty of Natural Science |

Qualifications: | PhD [Indian Institute of Technology Kanpur, India] |

Tel: | 021-9593917 |

Fax: | 021-9591241 |

Email: | kpatidar@uwc.ac.za |

Research: |

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 C2 rating (established researcher) from the South African National Research Foundation (NRF) for the period 2010-2015 and again for 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 and 2017-2019) 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 90 research articles (in journals of international standing), 6 invited book chapters, 11 papers in the proceedings of international conferences and 5 extended abstracts. He graduated 17 PhD and 16 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.

Administrative assignments:

Head of Department [Mathematics and Applied Mathematics, UWC]: From Jan 2018.

Deputy Head of Department [Mathematics and Applied Mathematics, UWC]: Jan 2014 - Dec 2017.

Member of the Joint Appointments and Promotions Committee of Senate and Council, UWC, Jan 2019 - Dec 2019.

Senate Research Committee [Representative from Science Faculty: July 2013 - Dec 2015]

Senate Scholarships and Fellowships Committee [Representative from Science Faculty: Jan 2014 - Dec 2019]

Member of the Executive Team of AIMS (African Institute for Mathematical Sciences) South Africa [2015 – 2020]

Member of Science Faculty's Professorial Appointments/Promotions Committee (Jan 2015 - )

Deputy Chair of Science Faculty's Higher Degrees Committee (2015)

Member of the Executive Committee of Science Faculty's Higher Degrees Committee (from Jan 2014)

Member of the Executive Committee of Science Faculty's Post-Graduate Committee (Jan 2011 - Dec 2013)

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].

**Summary as of 09 January 2020: **Google Scholar [Citations: 1418 (all), 772 (since 2015); h-index: 22 (all), 15 (since 2015); i10-index: 47 (all), 27 (since 2015)]; MathSciNet (Publications: 95; Citations: 305)]:

**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: **

- 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.
- 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.
- 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, Published online: 13 Nov 2018.
- 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.
- 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.
- 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, 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.
- 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, published online in 2013. DOI: 10.1093/imamat/hxt009.
- 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:**

- 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:**

**2 Post-Docs** (A Ramanantoanina and S Zergani).

**6 PhDs** (D Elago, M Dube, EM Adamu, GT
Affesa, YA Belay, Co-supervision: MT Sayi).

**2 MSc** (GAMO Farah, TD Tawe).

**Completed:**

**3 Post-Docs **(M Akanbi, A Meraj and J Munyakazi).

**17 PhD **(15 Main Supervision, 2
Co-Supervision): S Nuugulu (2020), A Shikongo (2020), CK Mbayi (2020), 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).

**12 MSc **((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).

**7 Accredited 30 credit Honours
projects **(KLV Awaseb, NN
Moyo, BD Coraizin, MG Constant, O Nkwinika, B Muhire and K Noganta).