一阶均值场博弈系统的拉格朗日-加勒金方案

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED SIAM Journal on Numerical Analysis Pub Date : 2024-01-16 DOI:10.1137/23m1561762

Elisabetta Carlini, Francisco J. Silva, Ahmad Zorkot

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引用次数: 0

摘要

SIAM 数值分析期刊》第 62 卷第 1 期第 167-198 页，2024 年 2 月。摘要在这项工作中，我们考虑了一个具有非局部耦合的一阶均值场博弈系统。提出了连续性方程的拉格朗日-加勒金方案和汉密尔顿-雅各比-贝尔曼方程的半拉格朗日方案来离散均值场博弈系统。在任意空间维度上，确定了该方案的解向均值场博弈系统解的收敛性。该方案用于近似一维和二维的两个均值场博弈系统。

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A Lagrange–Galerkin Scheme for First Order Mean Field Game Systems

SIAM Journal on Numerical Analysis, Volume 62, Issue 1, Page 167-198, February 2024.
Abstract. In this work, we consider a first order mean field game system with nonlocal couplings. A Lagrange–Galerkin scheme for the continuity equation, coupled with a semi-Lagrangian scheme for the Hamilton–Jacobi–Bellman equation, is proposed to discretize the mean field games system. The convergence of solutions to the scheme towards a solution to the mean field game system is established in arbitrary space dimensions. The scheme is implemented to approximate two mean field games systems in dimensions one and two.

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来源期刊

SIAM Journal on Numerical Analysis 数学-应用数学

CiteScore

4.80

自引率

6.90%

发文量

110

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.