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

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 [8] 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 ε-uniform results. Furthermore we improve upon the analysis of [8] to show that, for small ε, just one iteration is required to achieve the expected accuracy