In this article, we propose a new approximate procedure based on He’s variational iteration method for solving nonlinear hyperbolic equations. We introduce two transformations q = ut and σ = ux and formulate a first-order system of equations. We can obtain the approximation solution for the scalar unknown u, time derivative q = ut and space derivative σ = ux, simultaneously. Finally, some examp...

In this paper, the variational iteration method proposed by Ji-Huan He is applied to solve both linear and nonlinear boundary value problems for fourth order integro-differential equations. The numerical results obtained with minimum amount of computation are compared with the exact solutions to show the efficiency of the method. The results show that the variational iteration method is of high...

In this paper, by considering the variational iteration method, a kind of explicit exact and numerical solutions to the Lienard equation is obtained, and the numerical solutions has been compared with their known theoretical solution. The variational iteration method is based on Lagrange multipliers for identification of optimal value of parameters in a functional. Using this method, it is poss...

In this paper, we apply a new method for solving system of partial differential equations within local fractional derivative operators. The approximate analytical solutions are obtained by using the local fractional Laplace variational iteration method, which is the coupling method of local fractional variational iteration method and Laplace transform. Illustrative examples are included to demo...

The variational iteration method (VIM) proposed by Ji-Haun He is a new analytical method tosolve linear and nonlinear equation. In this paper, the Variational Iteration Method (VIM) has been applied for solving Davey-Stewartson equations which arise as higher dimensional generalizations of the Nonlinear Shrodinger (NLS) equation, as well as from physical considerations [1]. Comparison the absol...

in this paper, the rayleigh's quotient and the inverse vector iteration method are presented. the latter approach helps to obtain the natural frequencies and mode shapes of a structure. inverse vector iteration method with shifting enables to determine the higher modes. some basic theorems of linear algebra are presented and extended to study the free vibration of structures. the variation...

This paper reveals the reliability and efficiency of two modified versions of variational iteration method (VIM) where He’s and Adomian’s polynomials have been inserted in the correction functional of the VIM. The comparison of the suggested algorithms has been made on sixth-order boundary value problems (BVPs) by converting them into systems of integral equations. The proposed modified version...