Parameter-uniform numerical methods for a class of singularly perturbed problems with a neumann boundary condition

P. A. Farrell, A. F. Hegarty, J. J. Miller, E. O’Riordan, G. I. Shishkin

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

The error generated by the classical upwind finite difference method on a uniform mesh, when applied to a class of singularly perturbed modelo rdinary differentiale quations with a singularly perturbed Neumann boundary condition, tends to infinity as the singular perturbation parameter tends to zero. Note that the exact solution is uniformly bounded with respect to the perturbation parameter. For the same classicalfini te difference operator on an appropriate piecewise–uniform mesh, it is shown that the numerical solutions converge, uniformly with respect to the perturbation parameter, to the exact solution of any problem from this class.

Original languageEnglish
Title of host publicationNumerical Analysis and Its Applications - 2nd International Conference, NAA 2000, Revised Papers
EditorsLubin Vulkov, Plamen Yalamov, Jerzy Waniewski
PublisherSpringer Verlag
Pages292-303
Number of pages12
ISBN (Print)9783540418146
DOIs
Publication statusPublished - 2001
Event2nd International Conference on Numerical Analysis and Its Applications, NAA 2000 - Rousse, Bulgaria
Duration: 11 Jun 200015 Jun 2000

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1988
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference2nd International Conference on Numerical Analysis and Its Applications, NAA 2000
Country/TerritoryBulgaria
CityRousse
Period11/06/0015/06/00

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