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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Acknowledgements
This work was supported by National Natural Science Foundation of China under Grant No. 12071195, AI and Big Data Funds under Grant No. 2019620005000775, Fundamental Research Funds for the Central Universities under Grant Nos. lzujbky-2021-it26 and lzujbky-2021-kb15, and NSF of Gansu under Grant No. 21JR7RA537.
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Sun, J., Deng, W. & Nie, D. Numerical Approximations for the Fractional Fokker–Planck Equation with Two-Scale Diffusion. J Sci Comput 91, 34 (2022). https://doi.org/10.1007/s10915-022-01812-z
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DOI: https://doi.org/10.1007/s10915-022-01812-z