ON THE NON-EXISTENCE OF ε-UNIFORM FINITE DIFFERENCE METHODS ON UNIFORM MESHES FOR SEMILINEAR TWO-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 semilinear two-point boundary value problem. It is proved that a scheme of this type with a frozen fitting factor cannot converge ε-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.

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