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

摘要

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 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.