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Volume 38, Issue 3
A Lifting Method for Fokker-Planck Equations with Drift-Admitting Jumps

Ningbo Guo, Yaming Chen & Xiaogang Deng

DOI: 10.4208/cmr.2022-0012

Commun. Math. Res., 38 (2022), pp. 431-448.

Published online: 2022-08

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  • 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.

  • Keywords

Fokker-Planck equation, drifting-admitting jump, lifting method, finite difference method.

  • AMS Subject Headings

65M06, 35L65, 35L81

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{CMR-38-431, author = {Guo , NingboChen , Yaming and Deng , Xiaogang}, title = {A Lifting Method for Fokker-Planck Equations with Drift-Admitting Jumps}, journal = {Communications in Mathematical Research }, year = {2022}, volume = {38}, number = {3}, pages = {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.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2022-0012}, url = {http://global-sci.org/intro/article_detail/cmr/20964.html} }
TY - JOUR T1 - A Lifting Method for Fokker-Planck Equations with Drift-Admitting Jumps AU - Guo , Ningbo AU - Chen , Yaming AU - Deng , Xiaogang JO - Communications in Mathematical Research VL - 3 SP - 431 EP - 448 PY - 2022 DA - 2022/08 SN - 38 DO - http://doi.org/10.4208/cmr.2022-0012 UR - https://global-sci.org/intro/article_detail/cmr/20964.html KW - Fokker-Planck equation, drifting-admitting jump, lifting method, finite difference method. AB -

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.

Guo , NingboChen , Yaming and Deng , Xiaogang. (2022). A Lifting Method for Fokker-Planck Equations with Drift-Admitting Jumps. Communications in Mathematical Research . 38 (3). 431-448. doi:10.4208/cmr.2022-0012
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