论文标题
平均野外游戏的高级方案
A high-order scheme for mean field games
论文作者
论文摘要
在本文中，我们为时间相关的平均现场游戏系统提出了一个高阶数值方案。该方案是通过结合拉格朗日 - 加勒金和半拉格朗日技术来构建的，与太空步骤相比，对于大的时间步长而稳定且稳定。我们为应用于Fokker-Planck方程的精确集成的Lagrange-Galerkin方案提供了收敛分析，我们提出了一个具有不精确集成的可实施版本。最后，我们通过两个平均野外游戏系统的数值近似来验证所提出的方案的收敛速率。
In this paper we propose a high-order numerical scheme for time-dependent mean field games systems. The scheme, which is built by combining Lagrange-Galerkin and semi-Lagrangian techniques, is consistent and stable for large time steps compared with the space steps. We provide a convergence analysis for the exactly integrated Lagrange-Galerkin scheme applied to the Fokker-Planck equation, and we propose an implementable version with inexact integration. Finally, we validate the convergence rate of the proposed scheme through the numerical approximation of two mean field games systems.
