A fast semi-implicit difference method for a nonlinear two-sided space-fractional diffusion equation with variable diffusivity coefficients

被引:52
作者
Chen, S. [1 ]
Liu, F. [2 ]
Jiang, X. [1 ]
Turner, I. [2 ]
Anh, V. [2 ]
机构
[1] Shandong Univ, Sch Math, Jinan 250100, Peoples R China
[2] Queensland Univ Technol, Sch Math Sci, Brisbane, Qld 4001, Australia
基金
中国国家自然科学基金;
关键词
Anomalous diffusion; Variable coefficients; Stability and convergence; Bi-conjugate gradient stabilized method; Fast Fourier transform; Toeplitz matrix; NUMERICAL APPROXIMATION; ANOMALOUS DIFFUSION; CONVERGENCE; STABILITY;
D O I
10.1016/j.amc.2014.08.031
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we derive a new nonlinear two-sided space-fractional diffusion equation with variable coefficients from the fractional Fick's law. A semi-implicit difference method (SIDM) for this equation is proposed. The stability and convergence of the SIDM are discussed. For the implementation, we develop a fast accurate iterative method for the SIDM by decomposing the dense coefficient matrix into a combination of Toeplitz-like matrices. This fast iterative method significantly reduces the storage requirement of O(n(2)) and computational cost of O(n(3)) down to n and O(n log n), where n is the number of grid points. The method retains the same accuracy as the underlying SIDM solved with Gaussian elimination. Finally, some numerical results are shown to verify the accuracy and efficiency of the new method. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码:591 / 601
页数:11
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