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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 214505, 11 pages
http://dx.doi.org/10.1155/2013/214505
Research Article

A Moving Mesh Method for Singularly Perturbed Problems

1Department of Mathematics, University of Swaziland, Private Bag 4, Kwaluseni M201, Swaziland
2Department of Mathematics and Applied Mathematics, University of Venda, Private Bag X5050, Thohoyandou, South Africa

Received 29 May 2013; Accepted 19 October 2013

Academic Editor: Chun-Gang Zhu

Copyright © 2013 Stephen T. Sikwila and Stanford Shateyi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A singularly perturbed time dependent convection diffusion problem is solved on a rectangular domain, using the moving mesh method which uses the equidistribution principle. The problem has a boundary at the steady state. It is shown that the numerical approximations generated by the moving mesh method converge uniformly with respect to the singular perturbation parameter. Theoretical results are obtained which are verified using numerical results.