Mathematics of Computation

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

Author(s): C. Clavero; J. L. Gracia; E. O'Riordan.
Journal: Math. Comp. 74 (2005), 1743-1758.
MSC (2000): Primary 65N06, 65N12, 65N15; Secondary 35J25
Posted: June 7, 2005
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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.

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Retrieve articles in Mathematics of Computation with MSC (2000): 65N06, 65N12, 65N15, 35J25

C. Clavero
Affiliation: Departamento de Matemática Aplicada, Universidad de Zaragoza, Zaragoza, Spain
Email: clavero@unizar.es

J. L. Gracia
Affiliation: Departamento de Matemática Aplicada, Universidad de Zaragoza, Teruel, Spain
Email: jlgracia@unizar.es

E. O'Riordan
Affiliation: School of Mathematical Sciences, Dublin City University, Glasnevin, Dublin 9, Ireland
Email: eugene.oriordan@dcu.ie

DOI: 10.1090/S0025-5718-05-01762-X
PII: S 0025-5718(05)01762-X
Keywords: Reaction-diffusion, uniform convergence, Shihskin mesh, second order
Received by editor(s): May 19, 2004
Posted: June 7, 2005
Additional Notes: This research was partially supported by the Diputación General de Aragón and the project MCYT/FEDER BFM2001--2521
Copyright of article: Copyright 2005, American Mathematical Society

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