A parameter robust second order numerical method for a singularly perturbed two-parameter problem

In this paper a second order monotone numerical method is constructed for a singularly perturbed ordinary differential equation with two small parameters affecting the convection and diffusion terms. The monotone operator is combined with a piecewise-uniform Shishkin mesh. An asymptotic error bound...

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Bibliographic Details
Published in:Applied numerical mathematics 2006-07, Vol.56 (7), p.962-980
Main Authors: Gracia, J.L., O'Riordan, E., Pickett, M.L.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations, boundary value problems
Sciences and techniques of general use
Second order
Shishkin mesh
Singular perturbation
Uniform convergence
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Summary:In this paper a second order monotone numerical method is constructed for a singularly perturbed ordinary differential equation with two small parameters affecting the convection and diffusion terms. The monotone operator is combined with a piecewise-uniform Shishkin mesh. An asymptotic error bound in the maximum norm is established theoretically whose error constants are shown to be independent of both singular perturbation parameters. Numerical results are presented which support the theoretical results.
ISSN:0168-9274
1873-5460
DOI:10.1016/j.apnum.2005.08.002