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

S. Chen, F. Liu, X. Jiang, I. Turner and V. Anh

Applied Mathematics and Computation, 2015, vol. 257, issue C, 591-601

Abstract: 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(n2) and computational cost of O(n3) down to n and O(nlogn), 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.

Keywords: Anomalous diffusion; Variable coefficients; Stability and convergence; Bi-conjugate gradient stabilized method; Fast Fourier transform; Circulant matrix; Toeplitz matrix (search for similar items in EconPapers)
Date: 2015
References: View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:257:y:2015:i:c:p:591-601

DOI: 10.1016/j.amc.2014.08.031

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