Analysis of splitting methods for solving a partial integro-differential Fokker-Planck equation

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 Chang-Cooper method for spatial discretization with the Strang-Marchuk splitting and first- and second-order time discretization methods. It is proved that the SIMEX scheme is second-order accurate, positive preserving, and conservative. Results of numerical experiments that validate the theoretical results are presented.