A numerical solution of open-loop Nash equilibrium in nonlinear differential games based on Chebyshev pseudospectral method

Nikooeinejad, Z.; Delavarkhalafi, Ali; Heydari, Mohammad

doi:10.1016/j.cam.2016.01.019

Cited by 25 publications

(11 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…An open-loop Nash equilibrium is characterized by introducing the Hamiltonian functions for formulating the first order necessary conditions of optimality for nonzero-sum differential games (1), and are introduced as the following [24]:…”

Section: Problem Statementmentioning

confidence: 99%

Numerical Solution of Open-Loop Nash Differential Games Based on the Legendre Tau Method

Banadaki¹,

Navidi²

2020

Games

View full text Add to dashboard Cite

In this paper, an efficient implementation of the Tau method is presented for finding the open-loop Nash equilibrium of noncooperative nonzero-sum two-player differential game problems with a finite-time horizon. Regarding this approach, the two-point boundary value problem derived from Pontryagin’s maximum principle is reduced to a system of algebraic equations that can be solved numerically. Finally, a differential game arising from bioeconomics among firms harvesting a common renewable resource is included to illustrate the accuracy and efficiency of the proposed method and a comparison is made with the result obtained by fourth order Runge–Kutta method.

show abstract

Section: Problem Statementmentioning

confidence: 99%

Numerical Solution of Open-Loop Nash Differential Games Based on the Legendre Tau Method

Banadaki¹,

Navidi²

2020

Games

View full text Add to dashboard Cite

show abstract

“…In this section, we briefly review the Chebyshev polynomials, generalized Laguerre polynomials, modified generalized Laguerre functions and Gauss-Legendre integration rule. For more details see [6,15,16,28,29,34,[36][37][38]41].…”

Section: Mathematical Preliminaries and Notationsmentioning

confidence: 99%

An improvement of Laguerre computational scheme for solving nonlinear age-structured population models

Avazzadeh¹,

Heydari²,

Yarahmadian³

2019

J. Math. Computer Sci.

View full text Add to dashboard Cite

In this paper, we simultaneously implement two kinds of orthogonal polynomials for solving a nonlinear age-structured population model. This non-classic type of partial differential equation is typically defined in large domains that makes finding an accurate solution by common techniques to be difficult. The presented method namely modified generalized Laguerre-Chebyshev (MGLC), which is based on the modified generalized Laguerre functions and Chebyshev orthogonal polynomials provides the spectral accuracy. The theoretical and experimental analysis of the scheme reliability verifies the validity of the proposed method in large domains.

show abstract

“…Also, Samadyar and Mirzaee introduced a meshfree method based on RBFs to solve two‐dimensional weakly singular stochastic integral equations. The system of nonlinear stochastic differential and integral equations is increasingly employed to model problems in finance, biology, medicine, physics, engineering, etc . For example, the multiple stock model in the financial markets, the linear and nonlinear pendulum problem in the physics, and the predator‐prey models in the some area of science are some applications of the SNSIVEs.…”

Section: Introductionmentioning

confidence: 99%

Convergence analysis of an iterative algorithm to solve system of nonlinear stochastic Itô‐Volterra integral equations

Saffarzadeh

Heydari

Loghmani

2020

Math Methods in App Sciences

View full text Add to dashboard Cite

In this paper, an efficient and accurate numerical iterative algorithm based on the linear spline interpolation for solving the system of nonlinear stochastic Itô-Volterra integral equations is presented. The most important merit of this method is that it does not need to solve any system of nonlinear algebraic equations. An upper bound for the linear spline approximation of the stochastic function is provided. Using this upper bound and under the Lipschitz and linear growth conditions, the convergence analysis of the suggested method is studied.Finally, to verify the efficiency of the proposed scheme, some problems in the finance, physics, and biology are investigated, and the obtained results are compared with the stochastic -method. KEYWORDSlinear spline interpolation, multiple stock models, pendulum problem, predator-prey models, successive approximations method, system of stochastic Volterra integral equations MSC CLASSIFICATION 60H10; 60H20; 65C30Math Meth Appl Sci. 2020;43:5212-5233. wileyonlinelibrary.com/journal/mma

show abstract

A numerical solution of open-loop Nash equilibrium in nonlinear differential games based on Chebyshev pseudospectral method

Cited by 25 publications

References 19 publications

Numerical Solution of Open-Loop Nash Differential Games Based on the Legendre Tau Method

Numerical Solution of Open-Loop Nash Differential Games Based on the Legendre Tau Method

An improvement of Laguerre computational scheme for solving nonlinear age-structured population models

Convergence analysis of an iterative algorithm to solve system of nonlinear stochastic Itô‐Volterra integral equations

Contact Info

Product

Resources

About