On a uniformly accurate finite difference approximation of a singularly perturbed reaction-diffusion problem using grid equidistribution

G. Beckett, J.A. Mackenzie

Research output: Contribution to journalArticle

59 Citations (Scopus)

Abstract

We examine the convergence properties of a finite difference approximation of a singularly perturbed reaction-diffusion boundary value problem using a nonuniform grid. The grid is based on the equidistribution of a positive monitor function that is a linear combination of a constant floor and a power of the second derivative of the solution. Analysis shows how the monitor function can be chosen to ensure that the accuracy of the numerical approximation is insensitive to the size of the singular perturbation parameter. The use of equidistribution principles appears in many practical grid adaption schemes and our analysis provides insight into the convergence behaviour on such grids. Numerical results are given that confirm the uniform convergence rates.
Original languageEnglish
Pages (from-to)381-405
Number of pages24
JournalJournal of Computational and Applied Mathematics
Volume131
Issue number1-2
DOIs
Publication statusPublished - 2001

Keywords

  • uniform convergence
  • adaptivity
  • equidistribution
  • singular perturbation
  • reaction-diffusion
  • computational mathematics

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