1. Open Access Kent State
  2. On the Non-Existence of [Epsilon]-Uniform Finite Difference Methods on Uniform Meshes for Semilinear Two-point Boundary Value Problems
Author(s)
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.
Format
Article
Publication Date
1998-04-01
Publication Title
Mathematics of Computation
Volume
67
Issue
222
First Page
603
Last Page
617
Subject
Community
Department of Computer Science
Comments

First published in Mathematics of Computation in 1998, published by the American Mathematical Society.
Permalink https://oaks.kent.edu/cspubs/12
Farrell, P., Miller, J., O’Riordan, E., & Shishkin, G. (1998). On the Non-Existence of [Epsilon]-Uniform Finite Difference Methods on Uniform Meshes for Semilinear Two-point Boundary Value Problems. Mathematics of Computation. https://oaks.kent.edu/node/1325
Farrell, Paul, John Miller, Eugene O’Riordan, and Grigori Shishkin. 1998. “On the Non-Existence of [Epsilon]-Uniform Finite Difference Methods on Uniform Meshes for Semilinear Two-Point Boundary Value Problems”. Mathematics of Computation. https://oaks.kent.edu/node/1325.
Farrell, P., J. Miller, E. O’Riordan, and G. Shishkin. On the Non-Existence of [Epsilon]-Uniform Finite Difference Methods on Uniform Meshes for Semilinear Two-Point Boundary Value Problems. Mathematics of Computation, 1 Apr. 1998, https://oaks.kent.edu/node/1325.