@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 = {<p style="text-align: justify;">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.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2018.s10},
url = {http://global-sci.org/intro/article_detail/nmtma/12476.html}
}