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 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.
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Communicated by Aihui Zhou.
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O’Riordan, E., Stynes, M. Numerical analysis of a strongly coupled system of two singularly perturbed convection–diffusion problems. Adv Comput Math 30, 101–121 (2009). https://doi.org/10.1007/s10444-007-9058-z
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DOI: https://doi.org/10.1007/s10444-007-9058-z