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- W2009849061 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 [H. MacMullen, J.J.H. Miller, E. O’Riordan, G.I. Shishkin, A second-order parameter-uniform overlapping Schwarz method for reaction-diffusion problems with boundary layers, J. Comput. Appl. Math. 130 (2001) 231–244] 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 the above-mentioned reference to show that, for small ε, just one iteration is required to achieve the expected accuracy." @default.
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- W2009849061 date "2009-08-01" @default.
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- W2009849061 title "A parameter-uniform Schwarz method for a coupled system of reaction–diffusion equations" @default.
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- W2009849061 doi "https://doi.org/10.1016/j.cam.2008.12.009" @default.
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