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 - <p style="text-align: justify;">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.</p>