期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 229, 期 21, 页码 8095-8104出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2010.07.011
关键词
Anomalous diffusion; Circulant and Toeplitz matrices; Fast finite difference methods; Fast Fourier transform; Fractional diffusion equations
资金
- National Science Foundation [EAR-0934747]
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.
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