Numerical approximation of Levy–Feller diffusion equation and its probability interpretation

Zhang, H., Liu, Fawang, & Anh, Vo V. (2007) Numerical approximation of Levy–Feller diffusion equation and its probability interpretation. Journal of Computational and Applied Mathematics, 206(2), pp. 1098-1115.

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Abstract

In this paper, we consider the Levy–Feller fractional diffusion equation, which is obtained from the standard diffusion equation by replacing the second-order space derivative with a Riesz–Feller derivative of order and skewness θ (|θ|min{α,2-α}). We construct two new discrete schemes of the Cauchy problem for the above equation with 0<α<1 and 1<α2, respectively. We investigate their probabilistic interpretation and the domain of attraction of the corresponding stable Levy distribution. Furthermore, we present a numerical analysis for the Levy–Feller fractional diffusion equation with 1<α<2 in a bounded spatial domain. Finally, we present a numerical example to evaluate our theoretical analysis.

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17 citations in Scopus
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14 citations in Web of Science®

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218 since deposited on 30 Oct 2007
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ID Code: 10482
Item Type: Journal Article
Refereed: Yes
Keywords: Numerical approximation, Levy–Feller diffusion, Riesz–Feller potential, Stable probability distributions, Markovian random walk, Stability and convergence
DOI: 10.1016/j.cam.2006.09.017
ISSN: 0377-0427
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Copyright Owner: Copyright 2007 Elsevier
Copyright Statement: Reproduced in accordance with the copyright policy of the publisher.
Deposited On: 30 Oct 2007 00:00
Last Modified: 29 Feb 2012 13:21

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