A parameter-uniform Schwarz method for a coupled system of reaction–diffusion equations
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- 作者：Meghan Stephens ; Niall Madden
- 关键词：Singularly perturbed ; Coupled system ; Domain decomposition
- 刊名：Journal of Computational and Applied Mathematics
- 出版年：2009
- 出版时间：15 August 2009
- 年：2009
- 卷：230
- 期：2
- 页码：360-370
- 全文大小：589 K
文摘
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.