We consider a system of Fokker-Planck-Kolmogorov (FPK) equations, where the dependence of the coefficients is nonlinear and nonlocal in time with respect to the unknowns. We propose a semi-Lagrangian type scheme. The scheme is first order, explicit, preserves non-negativity, conserves the mass and allows large time steps. We analyze the convergence of the scheme and we study its applicability in two examples. The first one concerns a single population model and it is a variation of the Hughes model for pedestrian dynamics. The second one concerns two populations Mean Field Games.
Joint work with Francisco Silva, Universitè de Limoges, France.