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.
Mathematics of Computation
First published in Mathematics of Computation in 1998, published by the American Mathematical Society.
Farrell, Paul A; Miller, John J. H.; O'Riordan, Eugene; Shishkin, Grigori I (1998). On the Non-Existence of [Epsilon]-Uniform Finite Difference Methods on Uniform Meshes for Semilinear Two-point Boundary Value Problems. Mathematics of Computation 67(222) 603-617. Retrieved from https://oaks.kent.edu/cspubs/12