A fitted numerical method for singularly perturbed parabolic reaction-diffusion problems
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Date
2013
Journal Title
Journal ISSN
Volume Title
Publisher
Spring Verlag
Abstract
This paper treats a time-dependent singularly perturbed reaction-diffusion problem. We semidiscretize the problem in time by means of the classical backward Euler method. We develop a fitted operator finite difference method (FOFDM) to solve the resulting set of linear problems (one at each time level). We prove that the underlying fitted operator satisfies the maximum principle. This result is then used in the error analysis of the FOFDM. The method is shown to be first order convergent in time and second order convergent in space, uniformly with respect to the perturbation parameter. We test the method on several numerical examples to confirm our theoretical findings.
Description
Keywords
Parabolic reaction-diffusion problems, Singular perturbations, Fitted operator finite difference methods, Error bounds, Uniform convergence
Citation
Munyakazi, J.B. & Patidar, K.C. (2013). A fitted numerical method for singularly perturbed parabolic reaction-diffusion problems. Computational and Applied Mathematics, 32: 509 – 519