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Volume 11, Issue 4
A Space-Time Petrov-Galerkin Spectral Method for Time Fractional Diffusion Equation

Changtao Sheng & Jie Shen

DOI: 10.4208/nmtma.2018.s10

Numer. Math. Theor. Meth. Appl., 11 (2018), pp. 854-876.

Published online: 2018-06

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  • Abstract

We develop in this paper a space-time Petrov-Galerkin spectral method for linear and nonlinear time fractional diffusion equations (TFDEs) involving either a Caputo or Riemann-Liouville derivative. Our space-time spectral method is based on generalized Jacobi functions (GJFs) in time and Fourier-like basis functions in space. A complete error analysis is carried out for both linear and nonlinear TFDEs. Numerical experiments are presented to demonstrate the effectiveness of the proposed method.

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@Article{NMTMA-11-854, author = {Changtao Sheng and Jie Shen}, title = {A Space-Time Petrov-Galerkin Spectral Method for Time Fractional Diffusion Equation}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2018}, volume = {11}, number = {4}, pages = {854--876}, abstract = {

We develop in this paper a space-time Petrov-Galerkin spectral method for linear and nonlinear time fractional diffusion equations (TFDEs) involving either a Caputo or Riemann-Liouville derivative. Our space-time spectral method is based on generalized Jacobi functions (GJFs) in time and Fourier-like basis functions in space. A complete error analysis is carried out for both linear and nonlinear TFDEs. Numerical experiments are presented to demonstrate the effectiveness of the proposed method.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2018.s10}, url = {http://global-sci.org/intro/article_detail/nmtma/12476.html} }
TY - JOUR T1 - A Space-Time Petrov-Galerkin Spectral Method for Time Fractional Diffusion Equation AU - Changtao Sheng & Jie Shen JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 854 EP - 876 PY - 2018 DA - 2018/06 SN - 11 DO - http://doi.org/10.4208/nmtma.2018.s10 UR - https://global-sci.org/intro/article_detail/nmtma/12476.html KW - AB -

We develop in this paper a space-time Petrov-Galerkin spectral method for linear and nonlinear time fractional diffusion equations (TFDEs) involving either a Caputo or Riemann-Liouville derivative. Our space-time spectral method is based on generalized Jacobi functions (GJFs) in time and Fourier-like basis functions in space. A complete error analysis is carried out for both linear and nonlinear TFDEs. Numerical experiments are presented to demonstrate the effectiveness of the proposed method.

Changtao Sheng and Jie Shen. (2018). A Space-Time Petrov-Galerkin Spectral Method for Time Fractional Diffusion Equation. Numerical Mathematics: Theory, Methods and Applications. 11 (4). 854-876. doi:10.4208/nmtma.2018.s10
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