Numerical Method for Singularly Perturbed Parabolic Equations in Unbounded Domains in the Case of Solutions Growing at Infinity
Abstract: An initial-boundary value problem is considered in an unbounded do- main on the x-axis for a singularly perturbed parabolic reaction-diffusion equation. For small values of the parameter ε, a parabolic boundary layer arises in a neighbourhood of the lateral part of the boundary. In this problem, the error of a discrete solution in the maximum norm grows without bound even for fixed values of the parameter ε. In the present paper, the proximity of solutions of the initial-boundary value problem and of its numerical approximations is considered. Using the method of special grids condensing in a neighbourhood of the boundary layer, a special finite difference scheme converging ε-uniformly in the weight maximum norm has been constructed.
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- Extent
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Online-Ressource
- Language
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Englisch
- Bibliographic citation
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Numerical Method for Singularly Perturbed Parabolic Equations in Unbounded Domains in the Case of Solutions Growing at Infinity ; volume:9 ; number:1 ; year:2009 ; pages:100-110
Computational methods in applied mathematics ; 9, Heft 1 (2009), 100-110
- Creator
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Shishkin, G. I.
- DOI
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10.2478/cmam-2009-0006
- URN
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urn:nbn:de:101:1-2410261621328.708257451613
- Rights
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
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15.08.2025, 7:31 AM CEST
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Associated
- Shishkin, G. I.
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