Table of Contents Author Guidelines Submit a Manuscript
Journal of Function Spaces and Applications
Volume 2013, Article ID 542897, 6 pages
http://dx.doi.org/10.1155/2013/542897
Research Article

Numerical Solutions of Singularly Perturbed Reaction Diffusion Equation with Sobolev Gradients

1Department of Mathematics and Statistics, McMaster University, Hamilton, ON, Canada L8S 4K1
2Department of Mathematics, University of the Punjab, Lahore 54590, Pakistan
3Department of Mathematics, Brock University, St. Catharines, ON, Canada L2S 3A1
4Department of Mathematics, University of Engineering and Technology, Lahore 54890, Pakistan

Received 31 May 2013; Accepted 14 September 2013

Academic Editor: Chengbo Zhai

Copyright © 2013 Nauman Raza and Asma Rashid Butt. 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

Critical points related to the singular perturbed reaction diffusion models are calculated using weighted Sobolev gradient method in finite element setting. Performance of different Sobolev gradients has been discussed for varying diffusion coefficient values. A comparison is shown between the weighted and unweighted Sobolev gradients in two and three dimensions. The superiority of the method is also demonstrated by showing comparison with Newton's method.