Numer. Math. Theor. Meth. Appl., 11 (2018), pp. 854-876.
Published online: 2018-06
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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} }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.