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Volume 47, Issue 3
High Accuracy Spectral Method for the Space-Fractional Diffusion Equations

Shuying Zhai, Dongwei Gui, Jianping Zhao & Xinlong Feng

DOI: 10.4208/jms.v47n3.14.03

J. Math. Study, 47 (2014), pp. 274-286.

Published online: 2014-09

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  • 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.

  • Keywords

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

  • AMS Subject Headings

35K55, 65M70, 65L06, 65L12

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

zhaishuying123456@163.com (Shuying Zhai)

guidwei@163.com (Dongwei Gui)

zhaojianping@126.com (Jianping Zhao)

fxlmath@xju.edu.cn (Xinlong Feng)

  • BibTex
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  • TXT
@Article{JMS-47-274, author = {Zhai , ShuyingGui , DongweiZhao , Jianping and Feng , Xinlong}, title = {High Accuracy Spectral Method for the Space-Fractional Diffusion Equations}, journal = {Journal of Mathematical Study}, year = {2014}, volume = {47}, number = {3}, pages = {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.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v47n3.14.03}, url = {http://global-sci.org/intro/article_detail/jms/9958.html} }
TY - JOUR T1 - High Accuracy Spectral Method for the Space-Fractional Diffusion Equations AU - Zhai , Shuying AU - Gui , Dongwei AU - Zhao , Jianping AU - Feng , Xinlong JO - Journal of Mathematical Study VL - 3 SP - 274 EP - 286 PY - 2014 DA - 2014/09 SN - 47 DO - http://doi.org/10.4208/jms.v47n3.14.03 UR - https://global-sci.org/intro/article_detail/jms/9958.html KW - Space-fractional diffusion equation, fractional Laplacian, Chebyshev collocation method, Fourier spectral method, implicit-explicit Runge-Kutta method. AB -

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.

Shuying Zhai, Dongwei Gui, Jianping Zhao & Xinlong Feng. (2019). High Accuracy Spectral Method for the Space-Fractional Diffusion Equations. Journal of Mathematical Study. 47 (3). 274-286. doi:10.4208/jms.v47n3.14.03
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