A. Ebrahimzadeh - Department of Educational Mathematics, Farhangian university, Tehran, Iran.

This essay considers an optimal control problem (OCP) governed by a system of Fredholm integral equations (FIE). In this paper, collocation approach with utilizing Lagrange polynomials is introduced to transform the OCP into a nonlinear programming problem (NLP). An efficient op-timization method in Mathematica software is utilized to solve NLP. The convergence analysis is discussed, which show the theoretical structure behind the propounded technique under some assumptions. In this es-say, computational outcomes are given to demonstrate the adaptability, forthrightness, and relationship of the calculations manufactured. A prac-tical real-world problem involving hanging chain in classical mechanic is also dissolved utilizing the approach proposed.

Collocation method, Lagrange polynomials, optimal control, System of Fredholm integral equation, Convergence Analysis