  We prove convergence of a variational formulation of the BDF2 method applied
to the non-linear Fokker-Planck equation. Our approach is inspired by the
JKO-method and exploits the differential structure of the underlying
$L^2$-Wasserstein space. The technique presented here extends and strengthens
the results of our own recent work on the BDF2 method for general metric
gradient flows in the special case of the non-linear Fokker-Planck equation:
firstly, we do not require uniform semi-convexity of the augmented energy
functional; secondly, we prove strong instead of merely weak convergence of the
time-discrete approximations; thirdly, we directly prove without using the
abstract theory of curves of maximal slope that the obtained limit curve is a
weak solution of the non-linear Fokker-Planck equation.
