USSR Computational Mathematics and Mathematical Physics
Applied Mathematics and Computation
Computational Mathematics and Mathematical Physics
Domain decomposition in boundary layers for singularly perturbed problems
Applied Numerical Mathematics - Auckl numerical ordinary differential equations (ANODE 98 workshop)
Journal of Computational and Applied Mathematics
Domain decomposition for a singularly perturbed parabolic problem with a convection-dominated term
Journal of Computational and Applied Mathematics
A uniformly convergent scheme for a system of reaction-diffusion equations
Journal of Computational and Applied Mathematics
A parameter-uniform Schwarz method for a coupled system of reaction-diffusion equations
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
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In this work, we consider a singularly perturbed parabolic problem of reaction-diffusion type. To solve this problem numerically we develop an overlapping Schwarz domain decomposition method, where we use the asymptotic behaviour of the exact solution for domain partitioning. We prove that the method gives uniform numerical approximations of first order in time and almost second order in space. Furthermore, we address the much faster convergence of the algorithm for small perturbation parameter @e. To be more specific, we prove that, when @e is small, just one iteration is required to achieve the desired accuracy. We then extend the method to a system of singularly perturbed parabolic problems of reaction-diffusion type. Numerical experiments support the theoretical results and demonstrate the effectiveness of the method.