An almost fourth order uniformly convergent domain decomposition method for a coupled system of singularly perturbed reaction-diffusion equations

Authors:
S. Chandra Sekhara Rao;Sunil Kumar
Affiliations:
-;-
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

Citing 5
Cited 1

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A parameter-uniform Schwarz method for a coupled system of reaction-diffusion equations

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A robust overlapping Schwarz domain decomposition algorithm for time-dependent singularly perturbed reaction-diffusion problems

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Abstract

We consider a system of M(=2) singularly perturbed equations of reaction-diffusion type coupled through the reaction term. A high order Schwarz domain decomposition method is developed to solve the system numerically. The method splits the original domain into three overlapping subdomains. On two boundary layer subdomains we use a compact fourth order difference scheme on a uniform mesh while on the interior subdomain we use a hybrid scheme on a uniform mesh. We prove that the method is almost fourth order @e-uniformly convergent. Furthermore, we prove that when @e is small, one iteration is sufficient to get almost fourth order @e-uniform convergence. Numerical experiments are performed to support the theoretical results.