Open Access

ARTICLE

Robust Numerical Scheme for Singularly Perturbed Parabolic Initial-Boundary-Value Problems on Equidistributed Mesh

Srinivasan Natesan¹, S. Gowrisankar²

1 Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati - 781 039, India.
2 Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati - 781 039, India.

Computer Modeling in Engineering & Sciences 2012, 88(4), 245-268. https://doi.org/10.3970/cmes.2012.088.245

Abstract

In this article, we propose a parameter-uniform computational technique to solve singularly perturbed parabolic initial-boundary-value problems exhibiting parabolic layers. The domain is discretized with a uniform mesh on the time direction and a nonuniform mesh obtained via equidistribution of a monitor function for the spatial variable. The numerical scheme consists of the implicit-Euler scheme for the time derivative and the classical central difference scheme for the spatial derivative. Truncation error, and stability analysis are carried out. Error estimates are derived, and numerical examples are presented.

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Keywords

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