In this project, i will introduce a variational scheme for solving Fokker Planck equation, which is known as JKO scheme. Consider a Fokker-Planck equation and we can convert the evolution of the solution into gradient flow in Wasserstein metric. The derivation and explaination are in Explaination.pdf.
In fact, the associate gradient flow problem can be solved by JKO scheme.
JKO scheme for Fokker-Planck equation is actually a optimization problem with linear constraints. In this project I use Douglas-Rachford algorithm.
Given a two bumps initial condition, one can see it eventually converges to global equilibrium.
Wuzhe Xu