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A parameter robust numerical method for a two dimensional reaction-diffusion problem.

Clavero, C. and Gracia, J.L. and O'Riordan, Eugene (2006) A parameter robust numerical method for a two dimensional reaction-diffusion problem. Mathematics of Computation, 74 (252). pp. 1743-1758. ISSN 0025-5718

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Abstract

In this paper a singularly perturbed reaction-diffusion partial differential equation in two space dimensions is examined. By means of an appropriate decomposition, we describe the asymptotic behaviour of the solution of problems of this kind. A central finite difference scheme is constructed for this problem which involves an appropriate Shishkin mesh. We prove that the numerical approximations are almost second order uniformly convergent (in the maximum norm) with respect to the singular perturbation parameter. Some numerical experiments are given that illustrate in practice the theoretical order of convergence established for the numerical method.

Item Type:Article (Published)
Refereed:Yes
Uncontrolled Keywords:reaction-diffusion; uniform convergence; shihskin mesh; second order;
Subjects:Mathematics > Differential equations
Mathematics > Applied Mathematics
DCU Faculties and Centres:DCU Faculties and Schools > Faculty of Science and Health > School of Mathematical Sciences
Publisher:American Mathematical Society
Official URL:http://dx.doi.org/10.1090/S0025-5718-05-01762-X
Use License:This item is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 3.0 License. View License
ID Code:11
Deposited On:26 Oct 2006 by DORAS Administrator. Last Modified 29 Jan 2009 16:28

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