Dr Edgard Ngounda is a Lecturer in the Department of Mathematical Sciences at the University of the Free State, South Africa. He obtained his PhD in Numerical Analysis and Computational Finance from the University of the Western Cape, following an MSc in Numerical Analysis and a BSc Honours degree in Mathematics from Stellenbosch University.

 His research lies broadly in numerical analysis, scientific computing, and applied mathematics, with particular emphasis on the development, analysis, and implementation of numerical methods for ordinary and partial differential equations. His research interests include finite difference methods, spectral and collocation methods, approximation theory, numerical linear algebra, and computational techniques for solving linear and nonlinear differential equations. He also has an active interest in inverse problems, Sobolev spaces, and approximation methods arising in modern numerical analysis. Computational finance remains an important application area of his research, particularly the numerical valuation of financial derivatives under stochastic volatility and jump-diffusion models.

Dr Ngounda has published in internationally recognised journals, including Applied Numerical Mathematics, Numerical Methods for Partial Differential Equations, Journal of Optimization Theory and Applications, Communications in Nonlinear Science and Numerical Simulation, and Electronic Transactions on Numerical Analysis. His research has contributed to the development of efficient algorithms based on contour integral methods, Laplace transform techniques, spectral approximations, and spline methods for solving challenging problems in computational mathematics.

At the University of the Free State, Dr Ngounda teaches undergraduate and postgraduate modules in calculus, optimization, numerical analysis, financial mathematics, complex analysis, and numerical methods for ordinary and partial differential equations. He has supervised Honours and Master`s students and is currently co-supervising doctoral research in numerical methods for option pricing. He is committed to developing research capacity in numerical analysis and mentoring postgraduate students pursuing careers in applied mathematics.

Dr Ngounda serves as a reviewer for several international journals, including Applied Mathematics and Computation, Applied Numerical Mathematics, and Computational Economics. He is a member of the South African Mathematical Society, and his current research seeks to advance robust and efficient numerical algorithms for differential equations arising in science, engineering, and finance.

• E. Pindza, K.C. Patidar and E. Ngounda, A fully spectral collocation methods for pricing European style standard and nonstandard options, Bulletin of Calcutta Mathematical Society, 107 (2015) 1-10.

• E. Ngounda, K.C. Patidar, Limitation and Improvements of standard spectral methods for pricing options,  International Journal of Advances in Engineering Sciences and Applied Mathematics, 7 (2015), 106-113.

• E. Pindza, K.C. Patidary 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: 4 (2014) 1169-1188.

• E. Ngounda, K.C. Patidar and E. Pindza, A Robust Spectral Method for Solving Heston’s Model, Journal of Optimization Theory and Applications, 161 (2014) 164-178, DOI10.1007/s10957-013-0284-x.

• Edgard Ngounda, Kailash Patidar, Edson Pindza, Contour Integral Method for European Options with Jumps, Communication in Nonlinear Science and Numerical Simulation, 18 (2013) 478–492

• 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 Transaction on Numerical Analysis, 18 (2013) 268-293

My research focuses on numerical analysis and scientific computing, particularly the development and analysis of efficient numerical methods for ordinary and partial differential equations. I am interested in approximation theory, spectral and finite difference methods, inverse problems, and computational mathematics, with applications to finance, physics, and engineering.

This broader statement aligns well with your teaching portfolio and leaves room for future work beyond computational finance, making it a stronger long-term academic profile.

• Numerical methods for linear and nonlinear PDEs
• Computational finance
• Approximation theory 

• MATW6824 (Financial mathematics)
• MATS6814 (Partial differential equations)
• MATM3714 (Complex analysis)
• MATA3764 (Industrial mathematics)
• MATA3774 (Numerical Analysis)