A Bernoulli Tau method for numerical solution of feedback Nash differential games with an error estimation

Document Type : Research Paper

Authors

Department of Applied Mathematics, Shahed University, Tehran, Iran.

Abstract

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.

Keywords

References

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Computational Methods for Differential Equations
Volume 10, Issue 4
October 2022
Pages 894-904

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History

  • Receive Date: 27 January 2021
  • Revise Date: 06 January 2022
  • Accept Date: 17 January 2022

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