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 - <p style="text-align: justify;">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.</p>