Comparison of PIM and the Variational Iteration Methods (VIM) for Solving Linear Optimal Control Problems

Comparison of PIM and the Variational Iteration Methods (VIM) for Solving Linear Optimal Control Problems

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 ...

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Solving nonlinear Volterra integro-differential equations via improvement of variational iteration method

Solving nonlinear Volterra integro-differential equations via improvement of variational iteration method

In this paper an efficient numerical method is proposed for solving the specific nonlinear Volterra integro-differential equation which is a combination of the variation iteration method and the spectral collocation method. This method is easy to implement and possesses the high-order accuracy. Illustrative examples are provided to illustrate the validity and reliability of the propose method. Numerical results obtained are compared favorably with the exact solutions. ...

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