Processing math: 100%
Journals
Resources
About Us
Open Access

A Fast Second-Order Finite Difference Method for Space-Fractional Diffusion Equations

A Fast Second-Order Finite Difference Method for Space-Fractional Diffusion Equations

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(N3) per time step and a memory of O(N2) 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(Nlog2N). Numerical experiments show the utility of the method.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

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.

Author Details

T. S. Basu

H. Wang