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On the Non-Existence of [Epsilon]-Uniform Finite Difference Methods on Uniform Meshes for Semilinear Two-point Boundary Value Problems
Mathematics of Computation
  • 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
4-1-1998
Document Type
Article
Disciplines
Abstract

In this paper fitted finite difference methods on a uniform mesh with internodal spacing h, are considered for a singularly perturbed semilinear two-point boundary value problem. It is proved that a scheme of this type with a frozen fitting factor cannot converge epsilon-uniformly in the maximum norm to the solution of the differential equation as the mesh spacing h goes to zero. Numerical experiments are presented which show that the same result is true, for a number of schemes with variable fitting factors.

Comments

First published in Mathematics of Computation in 1998, published by the American Mathematical Society.

Citation Information
Paul A Farrell, John J. H. Miller, Eugene O'Riordan and Grigori I. Shishkin. "On the Non-Existence of [Epsilon]-Uniform Finite Difference Methods on Uniform Meshes for Semilinear Two-point Boundary Value Problems" Mathematics of Computation Vol. 67 Iss. 222 (1998) p. 603 - 617
Available at: http://works.bepress.com/paul_farrell/2/