Volume 10, Issue 1
A Space-Time Petrov-Galerkin Spectral Method for Time Fractional Fokker-Planck Equation with Nonsmooth Solution

Wei Zeng, Aiguo Xiao, Weiping Bu, Junjie Wang & Shucun Li

East Asian J. Appl. Math., 10 (2020), pp. 89-105.

Published online: 2020-01

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  • 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 confifirm the theoretical error estimates.

  • Keywords

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

  • AMS Subject Headings

35R11, 35Q84, 65M70, 65M60, 65M12

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

xag@xtu.edu.cn (Aiguo Xiao)

  • BibTex
  • RIS
  • TXT
@Article{EAJAM-10-89, author = {Zeng , Wei and Xiao , Aiguo and Bu , Weiping and Wang , Junjie and Li , Shucun }, title = {A Space-Time Petrov-Galerkin Spectral Method for Time Fractional Fokker-Planck Equation with Nonsmooth Solution}, journal = {East Asian Journal on Applied Mathematics}, year = {2020}, volume = {10}, number = {1}, pages = {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 confifirm the theoretical error estimates.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.260119.140319}, url = {http://global-sci.org/intro/article_detail/eajam/13604.html} }
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://dor.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 confifirm the theoretical error estimates.

Wei Zeng, Aiguo Xiao, Weiping Bu, Junjie Wang & Shucun Li. (2020). A Space-Time Petrov-Galerkin Spectral Method for Time Fractional Fokker-Planck Equation with Nonsmooth Solution. East Asian Journal on Applied Mathematics. 10 (1). 89-105. doi:10.4208/eajam.260119.140319
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