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

• Autores: Meghan Stephens, Niall Madden
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 230, Nº 2, 2009, págs. 360-370
• Idioma: inglés
• DOI: 10.1016/j.cam.2008.12.009
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• Resumen

  • 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 e-uniform results. Furthermore we improve upon the analysis of the above-mentioned reference to show that, for small e, just one iteration is required to achieve the expected accuracy.