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 solution of the fractional hyperbolic partial differential equation is obtained by means of the variational iteration method. Our numerical results are compared with those obtained by the modified Gauss elimination method. Our results reveal that the technique introduced here is very effective, convenient, and quite accurate to one-dimensional fractional hyperbolic partial differential equa...

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, we introduce and study fuzzy variational-like inclusion, fuzzy resolvent equation and $h(cdot,cdot)$-$phi$-$eta$-accretive operator in real  uniformly smooth banach spaces. it is established that fuzzy variational-like inclusion is equivalent to a fixed point problem as well as to a fuzzy resolvent equation. this equivalence is used to define an iterative algorithm for solving fu...

He’s variational iteration method [1, 2], which is a modified general Lagrange multiplier method [3], has been shown to solve effectively, easily and accurately a large class of nonlinear problems with approximations which converge quickly to accurate solutions. It was successfully applied to autonomous ordinary differential equations [4], nonlinear partial differential equations with variable ...

the purpose of this study is to demonstrate the potential of imperialist competitivealgorithm (ica) for solving blasius dierential equation. this algorithm is inspiredby competition mechanism among imperialists and colonies and has demonstrated excellentcapabilities such as simplicity, accuracy, faster convergence and better global optimumachievement in contrast to other evolutionary algorithms...

In this paper, we apply the modified variational iteration method (mVIM) for solving integrodifferential equations and coupled systems of integro-differential equations. The proposed modification is made by the elegant coupling of He’s polynomials and the correction functional of variational iteration method. The proposed mVIM is applied without any discretization, transformation or restrictive...

In this work, we have applied the variational iteration method and He’s polynomials to solve partial differential equation (PDEs) with time-fractional derivative. The variational homotopy perturbation iteration method (VHPIM) is presented in two steps. Some illustrative examples are given in order to show the ability and simplicity of the approach. All numerical calculations in this manuscript ...