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Approximation of the Levy–Feller advection–dispersion process by random walk and finite difference method (2007)

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.

Publication details

Download	http://eprints.qut.edu.au/10478/
Publisher	Elsevier
Repository	ARROW Discovery Service (Australia)
Keywords	Levy–Feller advection–dispersion process, Finite difference approximation, Discrete random walk model, Stability analysis, Convergence analysis
Type	journal article
Relation	DOI:10.1016/j.jcp.2006.06.005, Liu, Q. and Liu, Fawang and Turner, Ian W. and 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.