NUI Galway Mathematics
Preprint IRL-GLWY-2008-001 (PDF)

A Parameter-Uniform Schwarz Method for a Coupled System of Reaction Diffusion Equations

M. Stephens and N. Madden.

Abstract

We consider an arbitrarily sized coupled system of one-dimensional reaction-diffusion problems that are singularly perturbed in nature. We describe an algorithm that uses a discrete Schwarz method on three overlapping subdomains, extending the method in [MacMullen et al, 2001] to a coupled system. On each subdomain we use a standard finite difference operator on a uniform mesh. We prove that when appropriate subdomains are used the method produces $\epsilon$-uniform results. Furthermore we improve the analysis of [MacMullen et al, 2001} to show that for small $\epsilon$ just one iteration is required.

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