Approximation of the Levy–Feller advection–dispersion process by random walk and finite difference method

Liu, Q., Liu, Fawang, Turner, Ian W., & Anh, Vo V. (2007) Approximation of the Levy–Feller advection–dispersion process by random walk and finite difference method. Journal of Computational Physics, 222(1), pp. 57-70.

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Abstract

In this paper we present a random walk model for approximating a Levy–Feller advection–dispersion process, governed by the Levy–Feller advection–dispersion differential equation (LFADE). We show that the random walk model converges to LFADE by use of a properly scaled transition to vanishing space and time steps. We propose an explicit finite difference approximation (EFDA) for LFADE, resulting from the Grunwald–Letnikov discretization of fractional derivatives. As a result of the interpretation of the random walk model, the stability and convergence of EFDA for LFADE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.

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ID Code: 10478
Item Type: Journal Article
Refereed: Yes
Additional Information: For more information, please refer to the journal’s website (see hypertext link) or contact the author.
Keywords: Levy–Feller advection–dispersion process, Finite difference approximation, Discrete random walk model, Stability analysis, Convergence analysis
DOI: 10.1016/j.jcp.2006.06.005
ISSN: 0021-9991
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Copyright Owner: Copyright 2007 Elsevier
Deposited On: 30 Oct 2007 00:00
Last Modified: 29 Feb 2012 18:00

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