ON THE NONEXISTENCE OF EPSILON-UNIFORM FINITE-DIFFERENCE METHODS ON UNIFORM MESHES FOR SEMILINEAR 2-POINT BOUNDARY-VALUE-PROBLEMS

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