Rate My Professor Kamalesh Kumar

Dr. Kumar specializes in numerical solutions of differential equations, particularly singularly perturbed convection-diffusion equations, time-delayed parabolic convection-diffusion problems, parabolic singularly perturbed partial differential equations with shift parameters, time-fractional singularly perturbed convection-diffusion problems, time-delayed singularly perturbed parabolic partial differential equations, singularly perturbed delay differential equations, and adaptive mesh methods for singularly perturbed differential-difference equations. His key publications include: K. Kumar and P.P. Chakravarthy, "A new stable finite difference scheme and its error analysis for two-dimensional singularly perturbed convection-diffusion equations," Numerical Methods for Partial Differential Equations, 38, 1215-1232 (2022); K. Kumar, P.P. Chakravarthy, P. Das and H. Ramos, "A graded mesh refinement approach for boundary layer originated in singularly perturbed time-delayed parabolic convection-diffusion problems," Mathematical Methods in the Applied Sciences, 44(16), 12332-12350 (2021); K. Kumar, P.P. Chakravarthy, H. Ramos and J. Vigo-Aguiar, "A stable finite difference scheme and error estimates for parabolic singularly perturbed PDEs with shift parameters," Journal of Computational and Applied Mathematics, 405, 113050 (2022); K. Kumar, P.P. Chakravarthy, H. Ramos and J. Vigo-Aguiar, "Numerical solution of time-fractional singularly perturbed convection-diffusion problem with a delay in time," Mathematical Methods in the Applied Sciences, 44(4), 3080-3097 (2021); and P.P. Chakravarthy and K. Kumar, "A new stable finite difference scheme and its convergence for time-delayed singularly perturbed parabolic PDEs," Computational and Applied Mathematics, 39(3), 140-156 (2020). He acts as a referee for journals including Applied Numerical Mathematics (Elsevier), Applied Mathematics & Computation (Elsevier), Mathematics and Computers in Simulation (Elsevier), Mathematical Modeling and Analysis, Examples and Counterexamples (Elsevier), and International Journal of Differential Equations (Hindawi).