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] .

中文翻译：

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具有分段恒定漂移的Fokker-Planck方程的解*

我们以分段恒定漂移研究Fokker-Planck方程的解，以漂移为两次跳跃的情况为例。拉普拉斯空间中的解可以用封闭解析形式表示，并且可以使用一些数值反演方法方便地求出其逆。通过数值反演获得的结果可以看作是精确的解，这使我们能够证明某些数值方法用于求解Fokker-Planck方程的有效性。特别是，我们以已解决的问题为例来说明先前提出的有限差分方案的五阶收敛速度[Chen Y and Deng X Phys。Rev.E 100（2019）053303]。