Finite difference upwind schemes for system of two coupled parabolic type of convection-diffusion equation with non-smooth terms

Abstract

In this work, efficient numerical approaches to the solution of a system of two coupled singularly perturbed parabolic type of convection-diffusion problem with discontinuous convection and source terms are designed using mixed finite difference operators on a piecewise-uniform Shishkin mesh is studied. Theoretically it is proved that our numerical method gives first-order converges uniformly at the discrete maximum norm. In the end, numerical results are provided to confirm the analytical error bounds.