Solution to the Fokker–Planck Equation with Piecewise-Constant Drift *
Bin Cheng1, Ya-Ming Chen2**, Xiao-Gang Deng2,3
1College of Computer, National University of Defense Technology, Changsha 410073, China 2College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China 3Chinese Academy of Military Science, Beijing 100071, China
Abstract：We study the solution to the Fokker–Planck equation with piecewise-constant drift, taking the case with two jumps in the drift as an example. The solution in Laplace space can be expressed in closed analytic form, and its inverse can be obtained conveniently using some numerical inversion methods. The results obtained by numerical inversion can be regarded as exact solutions, enabling us to demonstrate the validity of some numerical methods for solving the Fokker–Planck equation. In particular, we use the solved problem as a benchmark example for demonstrating the fifth-order convergence rate of the finite difference scheme proposed previously [Chen Y and Deng X Phys. Rev. E 100 (2019) 053303].
2020, Vol. 37 
