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A preconditioned fast finite difference method for space-time fractional partial differential equations

  • Hongfei fu EMAIL logo and Hong Wang
Published/Copyright: February 19, 2017

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.

Acknowledgements

The authors would like to express their sincere thanks to the referees for their very helpful comments and suggestions, which greatly improved the quality of this paper. This work was supported in part by the OSD/ARO MURI Grant W911NF-15-1-0562, by the National Science Foundation under Grants DMS-1216923 and DMS-1620194, by the National Natural Science Foundation of China under Grants 11201485, 91630207, 11471194 and 11571115, and by the Fundamental Research Funds for the Central Universities under Grants 14CX02217A and 16CX02050A, and by the China Scholarship Council under Grant 201506455014.

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Received: 2015-12-15
Revised: 2016-7-17
Published Online: 2017-2-19
Published in Print: 2017-2-1

© 2017 Diogenes Co., Sofia

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