Fourier Convergence Analysis for a Fokker-Planck Equation of Tempered Fractional Langevin-Brownian Motion
Year: 2024
Author: Maoping Wang, Weihua Deng
Numerical Mathematics: Theory, Methods and Applications, Vol. 17 (2024), Iss. 3 : pp. 751–776
Abstract
Fourier stability analysis works well and is popular for the finite difference schemes of the linear partial differential equations. However, there are less works on the Fourier convergence analysis, and many of the existing ones require unreasonable assumptions. After removing the assumptions, we provide rigorous Fourier convergence analyses for the equation with one time fractional derivative in our previous work. In the current work, by using different ideas, we propose the rigorous Fourier convergence analyses for the equation with several time fractional derivatives, i.e., the Fokker-Planck equation of tempered fractional Langevin-Brownian motion, still without the strong assumptions. The numerical experiments are performed to confirm the theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2023-0137
Numerical Mathematics: Theory, Methods and Applications, Vol. 17 (2024), Iss. 3 : pp. 751–776
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Time-fractional Fokker-Planck model L1-scheme stability Fourier convergence analysis.