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Advances in Computational Mathematics

, Volume 30, Issue 2, pp 101–121 | Cite as

Numerical analysis of a strongly coupled system of two singularly perturbed convection–diffusion problems

  • Eugene O’Riordan
  • Martin Stynes
Article

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.

Keywords

Singularly perturbed Convection–diffusion Coupled system Piecewise-uniform mesh 

Mathematics Subject Classifications (2000)

65L10 65L12 65L20 65L70 

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Copyright information

© Springer Science+Business Media, LLC. 2007

Authors and Affiliations

  1. 1.School of Mathematical SciencesDublin City UniversityDublin 9Ireland
  2. 2.Department of MathematicsNational University of IrelandCorkIreland

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