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Dehghan Banadaki, Mojtaba, Navidi, Hamidreza. (1401). A Bernoulli Tau method for numerical solution of feedback Nash differential games with an error estimation. سامانه مدیریت نشریات علمی, 10(4), 894-904. doi: 10.22034/cmde.2022.44213.1870
Mojtaba Dehghan Banadaki; Hamidreza Navidi. "A Bernoulli Tau method for numerical solution of feedback Nash differential games with an error estimation". سامانه مدیریت نشریات علمی, 10, 4, 1401, 894-904. doi: 10.22034/cmde.2022.44213.1870
Dehghan Banadaki, Mojtaba, Navidi, Hamidreza. (1401). 'A Bernoulli Tau method for numerical solution of feedback Nash differential games with an error estimation', سامانه مدیریت نشریات علمی, 10(4), pp. 894-904. doi: 10.22034/cmde.2022.44213.1870
Dehghan Banadaki, Mojtaba, Navidi, Hamidreza. A Bernoulli Tau method for numerical solution of feedback Nash differential games with an error estimation. سامانه مدیریت نشریات علمی, 1401; 10(4): 894-904. doi: 10.22034/cmde.2022.44213.1870

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

Computational Methods for Differential Equations
مقاله 4، دوره 10، شماره 4، دی 2022، صفحه 894-904    اصل مقاله (1.8 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2022.44213.1870
نویسندگان
Mojtaba Dehghan Banadaki؛ Hamidreza Navidi*
Department of Applied Mathematics, Shahed University, Tehran, Iran.
چکیده
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.
کلیدواژه‌ها
Differential games؛ Feedback Nash equilibrium؛ Bellman’s optimality principle؛ Bernoulli Tau method
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