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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:234

Article

Clavero, C.¹  Gracia, J. L.¹  Lisbona, F. J.¹ 

[1] Univ Zaragoza, Dept Appl Math, E-50009 Zaragoza, Spain

关键词: Reaction-diffusion systems;    High order;    Uniform convergence;    Shishkin mesh;    Hybrid HODIE methods;   

DOI  :  10.1016/j.cam.2010.03.011

来源: Elsevier

【 摘 要 】

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. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free