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.