Numerical analysis of a strongly coupled system of

Authors: Eugene O’Riordan Martin Stynes

Publish Date: 2007/11/21

Volume: 30, Issue: 2, Pages: 101-121

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Abstract

A system of two coupled singularly perturbed convection–diffusion ordinary differential equations is examined The diffusion term in each equation is multiplied by a small parameter and the equations are coupled through their convective terms The problem does not satisfy a conventional maximum principle Its solution is decomposed into regular and layer components Bounds on the derivatives of these components are established that show explicitly their dependence on the small parameter A numerical method consisting of simple upwinding and an appropriate piecewiseuniform Shishkin mesh is shown to generate numerical approximations that are essentially first order convergent uniformly in the small parameter to the true solution in the discrete maximum norm

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