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

Beckett, G. and Mackenzie, J.A. (2001) On a uniformly accurate finite difference approximation of a singularly perturbed reaction-diffusion problem using grid equidistribution. Journal of Computational and Applied Mathematics, 131 (1-2). pp. 381-405. ISSN 0377-0427

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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.

Item type: Article
ID code: 2007
Keywords: uniform convergence, adaptivity, equidistribution, singular perturbation, reaction-diffusion, computational mathematics, Mathematics, Computational Mathematics, Applied Mathematics
Subjects: Science > Mathematics
Department: Faculty of Science > Mathematics and Statistics
Related URLs:
    Depositing user: Strathprints Administrator
    Date Deposited: 16 Mar 2007
    Last modified: 04 Sep 2014 10:15
    URI: http://strathprints.strath.ac.uk/id/eprint/2007

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