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Discontinuity, Nonlinearity, and Complexity 5(2) (2016) 133--144 | DOI:10.5890/DNC.2016.06.003

Walid Abid$^{1}$, R. Yafia$^{2}$, M.A. Aziz-Alaoui$^{3}$, H. Bouhafa$^{1}$, A. Abichou$^{1}$

$^{1}$ Université de Carthage, Laboratoire d’ingenierie Mathématique EPT, Tunisia.

$^{2}$ Ibnou Zohr University, Polydisciplinary Faculty of Ouarzazate, B.P: 638, Ouarzazate, Morocco.

$^{3}$ Laboratoire de Mathématiques Appliqu´ees, 25 Rue Ph. Lebon, BP 540, 76058 Le Havre Cedex, France.

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Abstract

In this paper, a finite difference method for a non-linear reaction diffusion equation defined on a circular domain is presented. A simple second-order finite difference treatment of polar coordinate singularity for Laplacian operator, the centered difference approximations, the treatments for Neumann boundary problems are used to discretize this equation. By using this method, numerical solutions can be computed. In the end, we give two applications of reaction diffusion predator-prey models with modified Leslie-Gower and Holling type II functional responses.

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