TY - JOUR T1 - A Space-Time Petrov-Galerkin Spectral Method for Time Fractional Fokker-Planck Equation with Nonsmooth Solution AU - Zeng , Wei AU - Xiao , Aiguo AU - Bu , Weiping AU - Wang , Junjie AU - Li , Shucun JO - East Asian Journal on Applied Mathematics VL - 1 SP - 89 EP - 105 PY - 2020 DA - 2020/01 SN - 10 DO - http://doi.org/10.4208/eajam.260119.140319 UR - https://global-sci.org/intro/article_detail/eajam/13604.html KW - Time fractional Fokker-Planck equation, nonsmooth solution, generalised Jacobi functions, space-time Petrov-Galerkin spectral method, error estimate. AB -

An STPG spectral method for TFFP equations with nonsmooth solutions is developed. The numerical scheme is based on generalised Jacobi functions in time and Legendre polynomials in space. The generalised Jacobi functions match the leading singularity of the corresponding problem. Therefore, the method performs better than methods with polynomial bases. The stability and convergence of the method are proved. Numerical experiments confirm the theoretical error estimates.