A fully-discrete scheme for systems of nonlinear Fokker-Planck-Kolmogorov equations
This work provides a numerical method for systems of nonlinear Fokker-Planck-Kolmogorov equations, which is relevant for researchers in applied mathematics and physics modeling interacting populations or mean field games.
The authors extend a numerical scheme for a single nonlinear Fokker-Planck-Kolmogorov equation to systems of such equations, proving convergence and demonstrating applicability on two examples: a population model with two interacting species and two-population mean field games.
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 extend the numerical scheme proposed and studied recently by the authors for a single FPK equation of this type. We analyse the convergence of the scheme and we study its applicability in two examples. The first one concerns a population model involving two interacting species and the second one concerns two populations Mean Field Games.