A Fully-Discrete Scheme for Systems of Nonlinear Fokker-Planck-Kolmogorov Equations
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 in Carlini and Silva (SIAM J. Numer. Anal., 2018, To appear) 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.
KeywordsSystems of nonlinear Fokker-Planck-Kolmogorov equations Numerical Analysis Semi-Lagrangian schemes Markov chain approximation Mean Field Games
The first author acknowledges financial support by the Indam GNCS project “Metodi numerici per equazioni iperboliche e cinetiche e applicazioni”. The second author is partially supported by the ANR project MFG ANR-16-CE40-0015-01 and the PEPS-INSMI Jeunes project “Some open problems in Mean Field Games” for the years 2016 and 2017.
Both authors acknowledge financial support by the PGMO project VarPDEMFG.
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