In this paper we study a fully discrete Semi-Lagrangian approximation of a second order Mean Field Game system, which can be degenerate. We prove that the resulting scheme is well posed and, if the state dimension is equals to one, we prove a convergence result. Some numerical simulations are provided, evidencing the convergence of the approximation and also the difference between the numerical results for the degenerate and non-degenerate cases.
A Semi-Lagrangian scheme for a degenerate second order Mean Field Game system / Carlini, Elisabetta; Silva, Francisco J.. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - STAMPA. - 35:A(2015), pp. 4269-4292. [10.3934/dcds.2015.35.4269]
A Semi-Lagrangian scheme for a degenerate second order Mean Field Game system
Carlini, Elisabetta;Silva, Francisco J.
2015
Abstract
In this paper we study a fully discrete Semi-Lagrangian approximation of a second order Mean Field Game system, which can be degenerate. We prove that the resulting scheme is well posed and, if the state dimension is equals to one, we prove a convergence result. Some numerical simulations are provided, evidencing the convergence of the approximation and also the difference between the numerical results for the degenerate and non-degenerate cases.| File | Dimensione | Formato | |
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