Solving the Optimal Control Problems with Constraint of Integral Equations Via Müntz Polynomials

Abstract

In this study, an efficient numerical scheme is presented for solving a class of optimal control problems governed by the form of the Volterra-Fredholm integral equation. The technique based upon approximating the state and control functions by M¨untz polynomials. The numerical integration and new approach utilized to discretize the optimal control problem to a nonlinear programming using the Chebyshev nodes together with the Gauss quadrature rule. Finally, numerical examples illustrate the efficiency of the proposed method.

Key words and phrases. Optimal control problem, Class of Volterra-Fredholm Integral Equations, M¨untz-Legendre polynomial, Gauss-Legendre points, Gauss-Legendre quadrature.

2000 Mathematics Subject Classification. 49J21, 45G15