✦ LIBER ✦

A direct O(N log2 N) finite difference method for fractional diffusion equations

✍ Scribed by Hong Wang; Kaixin Wang; Treena Sircar

Book ID: 104020989
Publisher: Elsevier Science
Year: 2010
Tongue: English
Weight: 308 KB
Volume: 229
Category: Article
ISSN: 0021-9991
DOI: 10.1016/j.jcp.2010.07.011

No coin nor oath required. For personal study only.

✦ Synopsis

Fractional diffusion equations model phenomena exhibiting anomalous diffusion that can not be modeled accurately by the second-order diffusion equations. Because of the nonlocal property of fractional differential operators, the numerical methods have full coefficient matrices which require storage of O(N 2 ) and computational cost of O(N 3 ) where N is the number of grid points.

In this paper we develop a fast finite difference method for fractional diffusion equations, which only requires storage of O(N) and computational cost of O(N log 2 N) while retaining the same accuracy and approximation property as the regular finite difference method. Numerical experiments are presented to show the utility of the method.

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A direct O(N&#xa0;log2&#xa0;N) finite difference method for fractional diffusion equations

✦ Synopsis

A direct O(N log2 N) finite difference method for fractional diffusion equations