A Space-Time Petrov-Galerkin Spectral Method for Time Fractional Fokker-Planck Equation with Nonsmooth Solution

Authors

  • Wei Zeng School of Mathematics and Computational Science & Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, Hunan 411105, China.
  • Aiguo Xiao School of Mathematics and Computational Science & Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, Hunan 411105, China.
  • Weiping Bu School of Mathematics and Computational Science & Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, Hunan 411105, China.
  • Junjie Wang School of Mathematics and Computational Science & Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, Hunan 411105, China.
  • Shucun Li School of Mathematics and Computational Science & Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, Hunan 411105, China.

DOI:

https://doi.org/10.4208/eajam.260119.140319

Keywords:

Time fractional Fokker-Planck equation, nonsmooth solution, generalised Jacobi functions, space-time Petrov-Galerkin spectral method, error estimate.

Abstract

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.

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Published

2020-05-04

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Issue

Vol. 10 No. 1 (2020)

Section

Articles