New Paper ‘Structure-preserving numerical methods for Fokker-Planck equations’ published in the Proceedings in Applied Mathematics and Mechanics

The paper Structure-preserving numerical methods for Fokker-Planck equations of Hanna Bartel, Joshua Lampert, and me has been published in the Proceedings in Applied Mathematics and Mechanics.

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.

The reproducibility repository is available on GitHub.

As usual, you can find the preprint on arXiv.