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A preconditioned Fast Finite Difference Method for Space-Time Fractional Partial Differential Equations

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Abstract

We develop a fast space-time finite difference method for space-time fractional diffusion equations by fully utilizing the mathematical structure of the scheme. A circulant block preconditioner is proposed to further reduce the computational costs. The method has optimal-order memory requirement and approximately linear computational complexity. The method is not lossy, as no compression of the underlying numerical scheme has been employed. Consequently, the method retains the stability, accuracy, and, in particular, the conservation property of the underlying numerical scheme. Numerical experiments are presented to show the efficiency and capacity of long time modelling of the new method.

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Authors and Affiliations

  1. College of Science, China University of Petroleum Qingdao, Shandong, 266580, China

    Hongfei Fu

  2. Department of Mathematics, University of South Carolina, Columbia, South Carolina, 29208, USA

    Hong Wang

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  1. Hongfei Fu
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  2. Hong Wang
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Fu, H., Wang, H. A preconditioned Fast Finite Difference Method for Space-Time Fractional Partial Differential Equations. FCAA 20, 88–116 (2017). https://doi.org/10.1515/fca-2017-0005

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