Mojtaba Dehghan Banadaki - Department of Applied Mathematics, Shahed University, Tehran, Iran.
Hamidreza Navidi - Department of Applied Mathematics, Shahed University, Tehran, Iran.

In the present study, an efficient combination of the Tau method with the Bernoulli polynomials is proposed for computing the Feedback Nash equilibrium in differential games over a finite horizon. By this approach, the system of Hamilton-Jacobi Bellman equations of a differential game derived from Bellman’s optimality principle is transferred to a nonlinear system of algebraic equations solvable by using Newton’s iteration method. Some illustrative examples are provided to show the accuracy and efficiency of the proposed numerical method.

Differential games, Feedback Nash equilibrium, Bellman’s optimality principle, Bernoulli Tau method