A direct O(Nlog2N) finite difference method for fractional diffusion equations

被引：306

作者：

Wang, Hong ^{[1
,2
]}

Wang, Kaixin ^{[1
]}

Sircar, Treena ^{[2
]}

机构：

[1] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China

[2] Univ S Carolina, Dept Math, Columbia, SC 29208 USA

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2010年 / 229卷 / 21期

基金：

美国国家科学基金会;

关键词：

Anomalous diffusion; Circulant and Toeplitz matrices; Fast finite difference methods; Fast Fourier transform; Fractional diffusion equations; NUMERICAL APPROXIMATION; SPACE; TRANSPORT; STABILITY;

D O I：

10.1016/j.jcp.2010.07.011

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

Fractional diffusion equations model phenomena exhibiting anomalous diffusion that can not be modeled accurately by the second-order diffusion equations. Because of the non-local 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( Nlog(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. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：8095 / 8104

页数：10

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