An almost third order finite difference scheme for singularly perturbed reaction-diffusion systems

Authors:
C. Clavero;J. L. Gracia;F. J. Lisbona
Affiliations:
Department of Applied Mathematics, University of Zaragoza, Spain;Department of Applied Mathematics, University of Zaragoza, Spain;Department of Applied Mathematics, University of Zaragoza, Spain
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

Citing 4
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Abstract

This paper addresses the numerical approximation of solutions to coupled systems of singularly perturbed reaction-diffusion problems. In particular a hybrid finite difference scheme of HODIE type is constructed on a piecewise uniform Shishkin mesh. It is proved that the numerical scheme satisfies a discrete maximum principle and also that it is third order (except for a logarithmic factor) uniformly convergent, even for the case in which the diffusion parameter associated with each equation of the system has a different order of magnitude. Numerical examples supporting the theory are given.