@Article{CMR-38-3, author = {Ningbo, Guo and Yaming, Chen and Xiaogang, Deng}, 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 = {https://global-sci.com/article/81491/a-lifting-method-for-fokker-planck-equations-with-drift-admitting-jumps} }