Year: 2022
Author: Ningbo Guo, Yaming Chen, Xiaogang Deng
Communications in Mathematical Research , Vol. 38 (2022), Iss. 3 : pp. 431–448
Abstract
We develop in this paper a lifting method for Fokker-Planck equations with drift-admitting jumps, such that high-order finite difference schemes can be constructed directly based on grids with pure solution points. To illustrate the idea, we present as an example the construction of a fifth-order finite difference scheme. The validity of the scheme is demonstrated by conducting numerical experiments for the cases with drift admitting one jump and two jumps, respectively. Additionally, by introducing a splitting technique, we show that the lifting method can be extended to high dimensions. In particular, a two-dimensional case is studied in details to show the effectiveness of the extension.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmr.2022-0012
Communications in Mathematical Research , Vol. 38 (2022), Iss. 3 : pp. 431–448
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Fokker-Planck equation drifting-admitting jump lifting method finite difference method.