A Lifting Method for Fokker-Planck Equations with Drift-Admitting Jumps

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.