Overlapping Schwarz Method for a Singularly Perturbed Convection-Diffusion Problems with Two Distinct Parameters

Abstract

In this paper, a system of singularly perturbed convection- diffusion problems with two distinct small parameters is considered. The problem is solved by using hybrid difference scheme on a Shishkin mesh. This proposed scheme is composed of central difference scheme in the layer region and midpoint scheme on outer region. It is shown that the method produces numerical approximations which converge in the maximum norm to the exact solution. Also we have proved that, when appropriate subdomains are used, the numerical approximations generated from the method are shown to be almost second-order uniformly convergent. Furthermore, it is shown that, the two iterations are sufficient to achieve the expected accuracy. Numerical results are presented in the end which support the theoretical results strongly.