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

摘要

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.