Splitting Methods for Fokker-Planck Equations Related to Jump-Diffusion Processes

A splitting implicit-explicit (SIMEX) scheme for solving a partial integro-differential Fokker-Planck equation related to a jump-diffusion process is investigated. This scheme combines the method of Chang-Cooper for spatial discretization with the Strang-Marchuk splitting and first- and second-order time discretization methods. It is proven that the SIMEX scheme is second-order accurate, positive preserving, and conservative. Results of numerical experiments that validate the theoretical results are presented. (This chapter is a summary of the paper Gaviraghi et al. (Appl Math Comput, 2017); all theoretical statements in this summary are proved in that reference.)