Approximation of Singularly Perturbed Parabolic Reaction-Diffusion Equations with Nonsmooth Data

Abstract: In this paper we consider the Dirichlet problem on a rectangle for singularly perturbed parabolic equations of reaction-diffusion type. The reduced (for ε = 0) equation is an ordinary differential equation with respect to the time variable; the singular perturbation parameter ε may take arbitrary values from the half-interval (0,1]. Assume that sufficiently weak conditions are imposed upon the coefficients and the right-hand side of the equation, and also the boundary function. More precisely, the data satisfy the Hölder continuity condition with a small exponent α and α/2 with respect to the space and time variables. To solve the problem, we use the known ε-uniform numerical method which was developed previously for problems with sufficiently smooth and compatible data. It is shown that the numerical solution converges ε-uniformly. We discuss also the behavior of local accuracy of the scheme in the case where the data of the boundary-value problem are smoother on a part of the domain of definition.

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• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch

References and Relationships

• Bibliographic citation: Approximation of Singularly Perturbed Parabolic Reaction-Diffusion Equations with Nonsmooth Data ; volume:1 ; number:3 ; year:2001 ; pages:298-315 ; Computational methods in applied mathematics ; 1, Heft 3 (2001), 298-315

Contributors, Places and Time

• Creator: Shishkin, Grigorii

Further information

• DOI: 10.2478/cmam-2001-0020
• URN: urn:nbn:de:101:1-2410261606363.516923000489
• Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.