A common way to numerically solve Fokker-Planck equations is the Chang-Cooper method in space combined with one of the Euler methods in time. However, the explicit Euler method is only conditionally positive, leading to severe restrictions on the time step to ensure positivity. On the other hand, the implicit Euler method is robust but nonlinearly implicit. Instead, we propose to combine the Chang-Cooper method with unconditionally positive Patankar-type time integration methods, since they are unconditionally positive, robust for stiff problems, only linearly implicit, and also higher-order accurate. We describe the combined approach, analyse it, and present a relevant numerical example demonstrating advantages compared to schemes proposed in the literature.

翻译：数值求解Fokker-Planck方程的常用方法是在空间上采用Chang-Cooper方法，在时间上结合欧拉方法之一。然而，显式欧拉方法仅具有条件正性，为保证正性需对时间步长施加严格限制。另一方面，隐式欧拉方法虽具有鲁棒性，但属于非线性隐式格式。为此，我们提出将Chang-Cooper方法与无条件正性的Patankar型时间积分方法相结合，因为这类方法具有无条件正性、对刚性问题的鲁棒性、仅需线性隐式求解，且能保持高阶精度。本文详细阐述了该组合方法，进行了理论分析，并通过典型数值算例展示了其相较于文献已有格式的优越性。