Structure preserving schemes for nonlinear Fokker-Planck equations with anisotropic diffusion

Nadia Loy, Mattia Zanella

Preprint arXiv, 2019.

In this work we propose novel numerical schemes for nonlinear Fokker-Planck-type equations with anisotropic diffusion matrix that preserve fundamental structural properties like non negativity of the solution, entropy dissipation and which guarantees an arbitrarily accurate approximation of the steady state of the problem. All the methods presented are at least second order accurate in the transient regimes and high order for large times. Applications of the schemes to models for collective phenomena and life sciences are considered, in these examples anomalous diffusion is often observed and must be taken into account in realistic models.