摘要
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].
作者
Bin Cheng
Ya-Ming Chen
Xiao-Gang Deng
程彬;陈亚铭;邓小刚(College of Computer,National University of Defense Technology,Changsha 410073,China;College of Aerospace Science and Engineering,National University of Defense Technology,Changsha 410073,China;Chinese Academy of Military Science,Beijing 100071,China)
基金
Supported by the National Natural Science Foundation of China(Grant Nos.11972370 and 61772542)。
