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Article
A Uniformly Convergent Finite Difference Scheme for a Singularly Perturbed Semilinear Equation
SIAM Journal on Numerical Analysis
  • Paul A Farrell, Kent State University - Kent Campus
  • John J. H. Miller, Trinity College
  • Eugene O'Riordan, Dublin City University
  • Grigori I Shishkin, Russian Academy of Sciences
Publication Date
6-1-1996
Document Type
Article
Keywords
  • semilinear boundry value problem,
  • singular peturbation,
  • finite-difference scheme,
  • piecewise uniform mesh
Disciplines
Abstract
Boundary value problems for singularly perturbed semilinear elliptic equations are considered. Special piecewise-uniform meshes are constructed which yield accurate numerical solutions irrespective of the value of the small parameter. Numerical methods composed of standard monotone finite difference operators and these piecewise-uniform meshes are shown theoretically to be uniformly (with respect to the singular perturbation parameter) convergent. Numerical results are also presented, which indicate that in practice the method is first-order accurate.
Comments

Copyright 1996 Society for Industrial and Applied Mathematics.

Citation Information
Paul A Farrell, John J. H. Miller, Eugene O'Riordan and Grigori I Shishkin. "A Uniformly Convergent Finite Difference Scheme for a Singularly Perturbed Semilinear Equation" SIAM Journal on Numerical Analysis Vol. 33 Iss. 3 (1996) p. 1135 - 1149
Available at: http://works.bepress.com/paul_farrell/6/