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Research Article | Open Access

A transformed L 1 Legendre-Galerkin spectral method for time fractional Fokker-Planck equations

Diandian Huang1, Xin Huang1,2, Tingting Qin1,2, Yongtao Zhou3,4( )
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, China
Applied and Computational Mathematics Division, Beijing Computational Science Research Center, Beijing 100193, China
School of Science, Qingdao University of Technology, Qingdao 266033, China
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Abstract

The numerical solutions of time α-order ( α ∈ ( 0 , 1 ) ) Caputo fractional Fokker-Planck equations is considered. The constructed method is consist of the transformed L 1 ( T L 1) scheme in the temporal direction and the Legendre-Galerkin spectral method in the spatial direction. It has been shown that the T L 1 Legendre-Galerkin spectral method in L 2 -norm is exponential order convergent in space and ( 2 − α)-th order convergent in time. Several numerical examples are given to verify the obtained theoretical results.

Keywords

time fractional Fokker-Planck equationserror estimateLegendre-Galerkin spectral methodtransformed L1 schemechange of variable

References

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Networks and Heterogeneous Media
Volume 18 Issue 2,
June 2023
Pages 799-812
DOI: 10.3934/nhm.2023034

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Cite this article:
Huang D, Huang X, Qin T, et al. A transformed L 1 Legendre-Galerkin spectral method for time fractional Fokker-Planck equations. Networks and Heterogeneous Media, 2023, 18(2): 799-812. https://doi.org/10.3934/nhm.2023034

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Received: 19 December 2022
Revised: 12 February 2023
Accepted: 23 February 2023
Published: 15 June 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)