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High Accuracy Spectral Method for the Space-Fractional Diffusion Equations

High Accuracy Spectral Method for the Space-Fractional Diffusion Equations
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Year:    2014

Author:    Shuying Zhai, Dongwei Gui, Jianping Zhao, Xinlong Feng

Journal of Mathematical Study, Vol. 47 (2014), Iss. 3 : pp. 274–286

Abstract

In this paper, a high order accurate spectral method is presented for the space-fractional diffusion equations. Based on Fourier spectral method in space and  Chebyshev collocation method in time, three high order accuracy schemes are proposed. The main advantages of this method are that it yields a fully diagonal representation of the fractional operator, with increased accuracy and efficiency compared with low-order counterparts, and a completely straightforward extension to high spatial dimensions. Some numerical examples, including Allen-Cahn equation, are conducted to verify the effectiveness of this method.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jms.v47n3.14.03

Journal of Mathematical Study, Vol. 47 (2014), Iss. 3 : pp. 274–286

Published online:    2014-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    13

Keywords:    Space-fractional diffusion equation fractional Laplacian Chebyshev collocation method Fourier spectral method implicit-explicit Runge-Kutta method.

Author Details

Shuying Zhai

Dongwei Gui

Jianping Zhao

Xinlong Feng

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