Numerical Analysis of Singularly Perturbed System of parabolic convection-diffusion IBVP system with boundary layers

Abstract

In this paper, we get the numerical solution of a singularly perturbed system of boundary layer-exhibiting parabolic convection-diffusion problems. The backward-Euler method and an upwind finite difference scheme make up the suggested numerical approach for the time and spatial derivatives, respectively. For the spatial discretization, we analyse the scheme on a piecewise uniform Shishkin mesh in order to establish uniform convergence with regard to the perturbation parameters. The stability analysis for the suggested method is provided, and a parameter-uniform error estimate is generated. We have conducted some numerical tests to verify the theoretical findings.