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M. Yamaguti and S. Ushiki, “Chaos in Numerical Analysis of Ordinary Differential Equations,” Physica D: Nonlinear Phenomena, Vol. 3, No. 3, 1981, pp. 618-626. doi:10.1016/0167-2789(81)90044-0

has been cited by the following article:

• TITLE: Parametric Iteration Method for Solving Linear Optimal Control Problems

  AUTHORS: Abdolsaeed Alavi, Aghileh Heidari

  KEYWORDS: Parametric Iteration Method; Optimal Control Problem; Pontryagin’s Maximum Principle; He’s Variational Iteration Method

  JOURNAL NAME: Applied Mathematics, Vol.3 No.9, September 27, 2012

  ABSTRACT: This article presents the Parametric Iteration Method (PIM) for finding optimal control and its corresponding trajectory of linear systems. Without any discretization or transformation, PIM provides a sequence of functions which converges to the exact solution of problem. Our emphasis will be on an auxiliary parameter which directly affects on the rate of convergence. Comparison of PIM and the Variational Iteration Method (VIM) is given to show the preference of PIM over VIM. Numerical results are given for several test examples to demonstrate the applicability and efficiency of the method.