Title: Structure preserving schemes for nonlinear Fokker-Planck equations and applications,
Abstract: In this paper we focus on the construction of numerical schemes for nonlinear
Fokker-Planck equations that preserve the structural properties, like non
negativity of the solution, entropy dissipation and large time behavior. The
methods here developed are second order accurate, they do not require any
restriction on the mesh size and are capable to capture the asymptotic steady
states with arbitrary accuracy. These properties are essential for a correct
description of the underlying physical problem. Applications of the schemes to
several nonlinear Fokker-Planck equations with nonlocal terms describing
emerging collective behavior in socio-economic and life sciences are presented.