Richardson extrapolation technique for singularly perturbed system of parabolic partial differential equations with exponential boundary layers

摘要

In this article, we propose a higher-order uniformly convergent numerical scheme for singularly perturbed system of parabolic convection-diffusion problems exhibiting overlapping exponential boundary layers. It is well-known that the the numerical scheme consists of the backward-Euler method for the time derivative on uniform mesh and the classical upwind scheme for the spatial derivatives on a piecewise-uniform Shishkin mesh converges uniformly with almost first-order in both space ant time. Richardson extrapolation technique improves the accuracy of the above mentioned scheme from first-order to second-order uniformly convergent in both time and space. This has been proved mathematically in this article. In order to validate the theoretical results, we carried out some numerical experiments. (C) 2018 Elsevier Inc. All rights reserved.