Аннотация:We consider a problem described by Mean Field Games (MFG) and optimal Control theory on finite time horizon. This problem consists of a system pf PDEs: a kolmogorov-Fokker-Planck equation, evolving forward in time and a Hamilton-Jacobi-Bellman equation, evolving backwards in time. The difficulties related to the numerical solution come from a turnpike effect. We present a regularization method of this system of PDEs in a form of the extremal problem and introduce its numerical solution.