Year: 2020
Author: Maohua Ran, Chengjian Zhang
Journal of Computational Mathematics, Vol. 38 (2020), Iss. 2 : pp. 239–253
Abstract
In this paper, an efficient numerical method for solving the general fractional diffusion equations with Riesz fractional derivative is proposed by combining the fractional compact difference operator and the boundary value methods. In order to efficiently solve the generated linear large-scale system, the generalized minimal residual (GMRES) algorithm is applied. For accelerating the convergence rate of the iterative, the Strang-type, Chan-type and P-type preconditioners are introduced. The suggested method can reach higher order accuracy both in space and in time than the existing methods. When the used boundary value method is $A_{k1,k2}$-stable, it is proven that Strang-type preconditioner is invertible and the spectra of preconditioned matrix is clustered around 1. It implies that the iterative solution is convergent rapidly. Numerical experiments with the absorbing boundary condition and the generalized Dirichlet type further verify the efficiency.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1805-m2017-0081
Journal of Computational Mathematics, Vol. 38 (2020), Iss. 2 : pp. 239–253
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Boundary value method Circulant preconditioner High accuracy Generalized Dirichlet type boundary condition.
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