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 - <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>