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.

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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