An Almost Fourth Order Parameter-Robust Numerical Method for a Linear System of ($M\geq2$) Coupled Singularly Perturbed Reaction-Diffusion Problems
Year: 2013
Author: S. C. S. Rao, M. Kumar
International Journal of Numerical Analysis and Modeling, Vol. 10 (2013), Iss. 3 : pp. 603–621
Abstract
We present a high order parameter-robust finite difference method for a linear system of ($M\geq2$) coupled singularly perturbed reaction-diffusion two point boundary value problems. The problem is discretized using a suitable combination of the fourth order compact difference scheme and the central difference scheme on a generalized Shishkin mesh. A high order decomposition of the exact solution into its regular and singular parts is constructed. The error analysis is given and the method is proved to have almost fourth order parameter robust convergence, in the maximum norm. Numerical experiments are conducted to demonstrate the theoretical results.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2013-IJNAM-585
International Journal of Numerical Analysis and Modeling, Vol. 10 (2013), Iss. 3 : pp. 603–621
Published online: 2013-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Parameter-robust convergence System of coupled reaction-diffusion problem Generalized-Shishkin mesh Fourth order compact difference scheme Central difference scheme.