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Journal of Scientific Computing

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01-05-2022

Numerical Approximations for the Fractional Fokker–Planck Equation with Two-Scale Diffusion

Authors: Jing Sun, Weihua Deng, Daxin Nie

Published in: Journal of Scientific Computing | Issue 2/2022

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Abstract

Fractional Fokker–Planck equation plays an important role in describing anomalous dynamics. To the best of our knowledge, the existing numerical discussions mainly focus on this kind of equation involving one diffusion operator. In this paper, we first derive the fractional Fokker–Planck equation with two-scale diffusion from the Lévy process framework, and then the fully discrete scheme is built by using the \(L_{1}\) scheme for time discretization and finite element method for space. With the help of the sharp regularity estimate of the solution, we optimally get the spatial and temporal error estimates. Finally, we validate the effectiveness of the provided algorithm by extensive numerical experiments.

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Title: Numerical Approximations for the Fractional Fokker–Planck Equation with Two-Scale Diffusion
Authors: Jing Sun
Weihua Deng
Daxin Nie
Publication date: 01-05-2022
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 2/2022
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-022-01812-z

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