A numerical method for a system of singularly perturbed reaction-diffusion equations

Authors:
S. Matthews;E. O'Riordan;G. I. Shishkin
Affiliations:
School of Mathematical Sciences, Dublin City University, Dublin, Ireland;School of Mathematical Sciences, Dublin City University, Dublin, Ireland;Institute for Mathematics & Mechanics, Russian Academy of Sciences, Ekaterinburg, Russia
Venue:
Journal of Computational and Applied Mathematics
Year:
2002

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Abstract

A Dirichlet problem for a system of two coupled singularly perturbed reaction-diffusion ordinary differential equations is examined. A numerical method whose solutions converge pointwise at all points of the domain independently of the singular perturbation parameters is constructed and analysed. Numerical results are presented, which illustrate the theoretical results.