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An Iterative Numerical Algorithm for a Strongly Coupled System of Singularly Perturbed Convection-Diffusion Problems

  • E. O’Riordan
  • J. Stynes
  • M. Stynes
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5434)

Abstract

An iterative numerical method is constructed for a coupled system of singularly perturbed convection-diffusion-reaction two-point boundary value problems. It combines a standard finite difference operator with a piecewise-uniform Shishkin mesh, and uses a Jacobi-type iteration to compute a solution. Under certain assumptions on the coefficients in the differential equations, a bound on the maximum-norm error in the computed solution is established; this bound is independent of the values of the singular perturbation parameter. Numerical results are presented to illustrate the performance of the numerical method.

Keywords

Singularly Perturb Diagonal Dominance Shishkin Mesh Iterative Numerical Method Singular Perturbation Parameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • E. O’Riordan
    • 1
  • J. Stynes
    • 2
  • M. Stynes
    • 3
  1. 1.School of Mathematical SciencesDublin City UniversityIreland
  2. 2.Department of ComputingCork Institute of TechnologyCorkIreland
  3. 3.Department of MathematicsNational University of IrelandCorkIreland

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