Year: 2012
Author: T. S. Basu, H. Wang
International Journal of Numerical Analysis and Modeling, Vol. 9 (2012), Iss. 3 : pp. 658–666
Abstract
Fractional diffusion equations provide an adequate and accurate description of transport processes that exhibit anomalous diffusion that cannot be modeled accurately by classical second-order diffusion equations. However, numerical discretizations of fractional diffusion equations yield full coefficient matrices, which require a computational operation of $O(N^3)$ per time step and a memory of $O(N^2)$ for a problem of size $N$. In this paper we develop a fast second-order finite difference method for space-fractional diffusion equations, which only requires memory of $O(N)$ and computational work of $O(N log^2 N)$. Numerical experiments show the utility of the method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2012-IJNAM-652
International Journal of Numerical Analysis and Modeling, Vol. 9 (2012), Iss. 3 : pp. 658–666
Published online: 2012-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 9
Keywords: circulant and Toeplitz matrix fast direct solver fast finite difference methods fractional diffusion equations.