Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
522263 | Journal of Computational Physics | 2007 | 14 Pages |
Abstract
In this paper we present a random walk model for approximating a Lévy–Feller advection–dispersion process, governed by the Lévy–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 Grünwald–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.
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science Applications
Authors
Q. Liu, F. Liu, I. Turner, V. Anh,