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

A Space-Time Petrov-Galerkin Spectral Method for Time Fractional Fokker-Planck Equation with Nonsmooth Solution
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Year:    2020

Author:    Wei Zeng, Aiguo Xiao, Weiping Bu, Junjie Wang, Shucun Li

East Asian Journal on Applied Mathematics, Vol. 10 (2020), Iss. 1 : pp. 89–105

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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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

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

East Asian Journal on Applied Mathematics, Vol. 10 (2020), Iss. 1 : pp. 89–105

Published online:    2020-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

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

Author Details

Wei Zeng

Aiguo Xiao

Weiping Bu

Junjie Wang

Shucun Li

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