The fundamental and numerical solutions of the Riesz space fractional reaction-dispersion equation

J Chen, Fawang Liu, Ian Turner, Vo Anh

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 beta in (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.

doi:10.1017/S1446181108000333

Keywords


: random walk, fractional derivatives, probability density,stability, convergence



DOI: http://dx.doi.org/10.21914/anziamj.v50i0.2345



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.