Numerical Method for a Dynamic Conflict Model of Environmental Pollution Problem

Marianna Troeva^* and Vasiliy Lukin

The dynamic conflict model of an environmental pollution problem is considered. This model is formalized by the noncooperative two-person differential game in Banach space with separated dynamics of the agents and continuous payoff functions depending on a game trajectory. In this paper we present a numerical method for the solution of the considered differential game. The numerical method is based on the dynamic programming approach and the finite difference method. Some numerical results are provided for two-dimensional dynamic conflict model of an environmental pollution problem.

Mathematics Subject Classification: 49N70 49N90 90C39 65M06

Keywords: Noncooperative differential games; Numerical methods, Environmental pollution

Minisymposion: Dynamic Programming Approach to Optimal Control Methods and Applications