A second-order parameter-uniform overlapping Schwarz method for reaction-diffusion problems with boundary layers

H. MacMullen, J. J.H. Miller, E. O'Riordan, G. I. Shishkin

Research output: Contribution to journalArticlepeer-review

Abstract

The problem of constructing a parameter-uniform numerical method for a singularly perturbed self-adjoint ordinary differential equation is considered. It is shown that a suitably designed discrete Schwarz method, based on a standard finite difference operator with a uniform mesh on each subdomain, gives numerical approximations which converge in the maximum norm to the exact solution, uniformly with respect to the singular perturbation parameter. This parameter-uniform convergence is shown to be essentially second order. That this new discrete Schwarz method is efficient in practice is demonstrated by numerical experiments.

Original languageEnglish
Pages (from-to)231-244
Number of pages14
JournalJournal of Computational and Applied Mathematics
Volume130
Issue number1-2
DOIs
Publication statusPublished - 1 May 2001
Externally publishedYes

Keywords

  • Parameter-uniform
  • Reaction-diffusion
  • Schwarz
  • Singularly perturbed

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