On the non-existence of 𝜀-uniform finite difference methods on uniform meshes for semilinear two-point boundary value problems

Abstract

In this paper fitted finite difference methods on a uniform mesh with internodal spacing h 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 ε \varepsilon -uniformly in the maximum norm to the solution of the differential equation as the mesh spacing h 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.