Mathematics of Computation
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.
Farrell, Paul A.; Miller, John J. H.; O'Riordan, Eugene; and 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 http://digitalcommons.kent.edu/cspubs/12