High Order varepsilon-Uniform Methods for Singularly Perturbed Reaction-Diffusion Problems

Authors:
J. L. Gracia;Francisco J. Lisbona;C. Clavero
Affiliations:
-;-;-
Venue:
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
Year:
2000

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Abstract

The central difference scheme for reaction-diffusion problems, when fitted Shishkin type meshes are used, gives uniformly convergent methods of almost second order. In this work, we construct HOC (High Order Compact) compact monotone finite difference schemes, defined on a priori Shishkin meshes, uniformly convergent with respect the diffusion parameter 驴, which have order three and four except for a logarithmic factor. We show some numerical experiments which support the theoretical results.