A uniformly convergent numerical method for a coupled system of two singularly perturbed linear reaction-diffusion problems |
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Authors: | Madden, Niall Stynes, Martin |
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Affiliation: | 1 Department of Mathematics, National University of Ireland Galway, Ireland 2 Department of Mathematics, National University of Ireland Cork, Ireland |
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Abstract: | A coupled system of two singularly perturbed linear reactiondiffusiontwo-point boundary value problems is examined. The leading termof each equation is multiplied by a small positive parameter,but these parameters may have different magnitudes. The solutionsto the system have boundary layers that overlap and interact.The structure of these layers is analysed, and this leads tothe construction of a piecewise-uniform mesh that is a variantof the usual Shishkin mesh. On this mesh central differencingis proved to be almost first-order accurate, uniformly in bothsmall parameters. Supporting numerical results are presentedfor a test problem. |
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Keywords: | singularly perturbed finite difference method reaction diffusion coupled system Shishkin mesh |
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