Parameter-Uniform Convergence for a Finite Difference Method for a Singularly Perturbed Linear Reaction-Diffusion System with Discontinuous Source Terms
Year: 2014
Author: M. paramasivam, J. J. H. Miller, S. Valarmathi
International Journal of Numerical Analysis and Modeling, Vol. 11 (2014), Iss. 2 : pp. 385–399
Abstract
A singularly perturbed linear system of second order ordinary differential equations of reaction-diffusion type with discontinuous source terms is considered. A small positive parameter multiplies the leading term of each equation. These singular perturbation parameters are assumed to be distinct. The components of the solution exhibit overlapping boundary and interior layers. A numerical method is constructed that uses a classical finite difference scheme on a piecewise uniform Shishkin mesh. It is proved that the numerical approximations obtained by this method are essentially first order convergent uniformly with respect to all of the perturbation parameters. Numerical illustrations are presented in support of the theory.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2014-IJNAM-533
International Journal of Numerical Analysis and Modeling, Vol. 11 (2014), Iss. 2 : pp. 385–399
Published online: 2014-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Singular perturbation problems system of differential equations reaction-diffusion equations discontinuous source terms overlapping boundary and interior layers classical finite difference scheme Shishkin mesh parameter-uniform convergence.