A robust domain decomposition method for singularly perturbed parabolic reaction-diffusion systems

Abstract

In this paper we develop and analyse a Schwarz waveform relaxation (SWR) based domain decomposition method for solving a coupled system of singularly perturbed parabolic reaction-diffusion problems with distinct small positive parameters. The proposed discrete SWR method is based on decomposing the original computational domain into five overlapping subdomains and employing the central difference scheme in spatial direction and the backward Euler scheme in time direction to solve subdomain problems in the iterative steps. Further, we use appropriate interface conditions between space-time subdomain and present the convergence analysis of the method. In particular, it is proved that the proposed method converges uniformly of almost second order in spatial direction and first order in time direction. Finally, some numerical experiments are conducted in support of the theoretical results.