An efficient numerical method for a system of singularly perturbed semilinear reaction-diffusion equations

Authors:
S. Chandra Sekhara Rao;Sunil Kumar
Affiliations:
Department of Mathematics, Indian Institute of Technology Delhi, New Delhi, India;Department of Mathematics, Indian Institute of Technology Delhi, New Delhi, India
Venue:
NMA'10 Proceedings of the 7th international conference on Numerical methods and applications
Year:
2010

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Abstract

In this work we consider a system of singularly perturbed semilinear reaction-diffusion equations. To solve this problem numerically, we construct a finite difference scheme of Hermite type, and combine this with standard central difference scheme in a special way on a piecewise-uniform Shishkin mesh. We prove that the method is third order uniformly convergent. Numerical experiments are conducted to demonstrate the efficiency of the present method.