THE FUNDAMENTAL AND NUMERICAL SOLUTIONS OF THE RIESZ SPACE-FRACTIONAL REACTION–DISPERSION EQUATION

Publisher： Cambridge University Press

E-ISSN： 1446-8735|50|1|45-57

ISSN： 1446-1811

Source： ANZIAM Journal, Vol.50, Iss.1, 2008-07, pp. : 45-57

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Abstract

A Riesz space-fractional reaction–dispersion equation (RSFRDE) is obtained from the classical reaction–dispersion equation (RDE) by replacing the second-order space derivative with a Riesz derivative of order β(1,2]. In this paper, using Laplace and Fourier transforms, we obtain the fundamental solution for a RSFRDE. We propose an explicit finite-difference approximation for a RSFRDE in a bounded spatial domain, and analyse its stability and convergence. Some numerical examples are presented.

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