Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4642566 | Journal of Computational and Applied Mathematics | 2007 | 18 Pages |
Abstract
In this paper, we consider the Lévy–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 α∈(0,2](α≠1) and skewness θθ (|θ|⩽min{α,2-α}|θ|⩽min{α,2-α}). We construct two new discrete schemes of the Cauchy problem for the above equation with 0<α<10<α<1 and 1<α⩽21<α⩽2, respectively. We investigate their probabilistic interpretation and the domain of attraction of the corresponding stable Lévy distribution. Furthermore, we present a numerical analysis for the Lévy–Feller fractional diffusion equation with 1<α<21<α<2 in a bounded spatial domain. Finally, we present a numerical example to evaluate our theoretical analysis.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
H. Zhang, F. Liu, V. Anh,