Numerical analysis of a strongly coupled system of two singularly perturbed convection–diffusion problems
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 piecewise-uniform 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.
KeywordsSingularly perturbed Convection–diffusion Coupled system Piecewise-uniform mesh
Mathematics Subject Classifications (2000)65L10 65L12 65L20 65L70
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