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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| ID Code: | 10482 |
|---|---|
| Item Type: | Journal Article |
| 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 |
| Last Modified: | 29 Feb 2012 23:21 |
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