Fitted mesh method for a weakly coupled system of singularly perturbed reaction–convection–diffusion problems with discontinuous source term

Abstract

In this article, a parameter-uniform numerical method for a weakly coupled system of singularly perturbed reaction–convection–diffusion problems with discontinuous source term containing two small parameters multiplied to the highest and second highest derivative is presented. A fitted mesh method using an upwind finite difference scheme on piecewise-uniform Shishkin mesh is constructed. Error analysis is undertaken and numerical results are provided to support the theoretical error bounds. Keywords: Singular perturbation problem, Reaction–convection–diffusion system, Fitted mesh method, Shishkin mesh, Discontinuous source term, Parameter-uniform