TY - JOUR
T1 - Fourier Convergence Analysis for a Fokker-Planck Equation of Tempered Fractional Langevin-Brownian Motion
AU - Wang , Maoping
AU - Deng , Weihua
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 751
EP - 776
PY - 2024
DA - 2024/08
SN - 17
DO - http://doi.org/10.4208/nmtma.OA-2023-0137
UR - https://global-sci.org/intro/article_detail/nmtma/23373.html
KW - Time-fractional Fokker-Planck model, L1-scheme, stability, Fourier convergence analysis.
AB - <p style="text-align: justify;">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.</p>