A Space-Time Petrov-Galerkin Spectral Method for Time Fractional Diffusion Equation

作者：Sheng, Changtao; Shen, Jie^*

来源：Numerical Mathematics: Theory, Methods and Applications , 2018, 11(4): 854-876.

DOI：10.4208/nmtma.2018.s10

• Fractional differential operator
• generalised Jacobi functions
• Fourier-like basis function
• space-time spectral method
• error analysis

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 are 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.

• 出版日期2018-11
• 单位厦门大学