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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A radial basis function (RBF) and collocation method with for solving the modified equal width equation

A radial basis function (RBF) and collocation method with for solving the modified equal width equation

In this paper, we examined the global collocation method using standard types ofradial basis function for numerical solution of the modified equal width (MEW)equation. The propagation of single solitons and the interaction of two solitary wavesare used to validate the method which is found to be accurate and efficient. ...

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Solving Vibration Equations of MDOF Systems by Modified Differential Transform Method

Solving Vibration Equations of MDOF Systems by Modified Differential Transform Method

Vibration equations of discrete multi-degrees-of-freedom (MDOF)structural systems is system of differential equations. In linear systems,the differential equations are also linear. Various analytical andnumerical methods are available for solving the vibration equations instructural dynamics. In this paper modified differential transformmethod (MDTM) as a semi-analytical approach is generalized for thesystem of differential equations and is utilized for solving the vibrationequations of MDOF ...

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Solving nth-Order Integro-Differential Equations Using the Combined Laplace Transform- homotopy perturbation Method

Solving nth-Order Integro-Differential Equations Using the Combined Laplace Transform- homotopy perturbation Method

In this paper , the Combined Laplace Transform- homotopy perturbation Method is used to solve nthorder integro-differential equations . The results show that the method is very simple and effective.Comparisonn with exact solution shows that the method is very effective and convenient for solvingintegral equations. ...

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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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