High Order Uniform Methods for a Singularly Perturbed Reaction-Diffusion Problems
by
José Luis Gracia
Departamento de Matemática Aplicada. Universidad de Zaragoza. Spain
Coauthors: Francisco J. Lisbona (Departamento de Matemática Aplicada. Universidad de Zaragoza. Spain), Carmelo Clavero (Departamento de Matemática Aplicada. Universidad de Zaragoza. Spain)

Uniformly convergent (with respect the diffusion parameter) methods of low order for singularly perturbed problems of reaction-diffusion type are well know. Nevertheless, it is interesting to dispose of robust high order methods. In this work we construct and analyze some compact monotone finite difference schemes with order three and four, except for a logarithmic factor, to solve this type of problems. The methods are defined on a priori Shishkin or Shishkin/Bakhvalov meshes, and they are deduced used the HOC (High Order Compact) technique. In this technique we incorporate to central difference scheme, which have order almost two, appropriate approximations of some terms of its truncation error. We show some numerical experiments which support the proved theoretical results.

Date received: February 10, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caen-19.