This paper investigates the implementation of Variational Iteration Method (VIM) to practical and higher order nonlinear equations in kind of Korteweg-de-Vries (KdV) equation. The obtained solutions from thirdand fourth-order modified KdV are compared with the exact and Homotopy Perturbation Method (HPM) solutions. Results illustrate the efficiency and capability of VIM to solve high order nonl...

In this paper, fractional complex transform (FCT) with help of variational iteration method (VIM) is used to obtain numerical and analytical solutions for the fractional Zakharov–Kuznetsov equations. Fractional complex transform (FCT) is proposed to convert fractional Zakharov– Kuznetsov equations to its differential partner and then applied VIM to the new obtained equations. Several examples a...

In this paper, using a model transformation approach a system of linear delay differential equations (DDEs) with multiple delays is converted to a non-delayed initial value problem. The variational iteration method (VIM) is then applied to obtain the approximate analytical solutions. Numerical results are given for several examples involving scalar and second order systems. Comparisons with the...

Responses of the dynamical systems are highly affected by the natural frequencies and it has a huge impact on design and operation of high-rise and high-speed elevators. In the present paper, the variational iteration method (VIM) is employed to investigate better understanding the dynamics of elevator cable as a single-degree-of-freedom (SDOF) swing system. Comparisons made among the results o...

We present a new numerical method to get the approximate solutions of fractional differential equations. A new operational matrix of integration for fractional-order Legendre functions (FLFs) is first derived. Then a modified variational iteration formula which can avoid "noise terms" is constructed. Finally a numerical method based on variational iteration method (VIM) and FLFs is developed fo...

A comparative study is presented about the Adomian’s decomposition method (ADM), variational iteration method (VIM), and fractional variational iteration method (FVIM) in dealing with fractional partial differential equations (FPDEs).The study outlines the significant features of the ADM and FVIMmethods. It is found that FVIM is identical to ADM in certain scenarios. Numerical results from thre...

The famous Perona-Malik (P-M) equation which was at first introduced for image restoration has been solved via various numerical methods. In this paper we will solve it for the first time via applying a new numerical method called the Variational Iteration Method (VIM) and the correspondent approximated solutions will be obtained for the P-M equation with regards to relevant error analysis. Thr...

In this paper, a new reliable method called the step variational iteration method (SVIM) based on an adaptation of the variational iteration method (VIM) is presented to solve non–chaotic and chaotic systems. The SVIM uses the general Lagrange multipliers for constructing the correction functional for the problems. The SVIM yields a step analytical solution of the form of a rapidly convergent i...

Abstract. One of the newest analytical methods to solve nonlinear dispersive wave equations is using both homotopy and perturbation methods which is called (HPM). Other the reliable methods are variational iteration method (VIM) by He and Adomian's decomposition method (ADM). Here, we compare the exact solution of HPM which are applied to solve a various fifth-order Korteweg-de Vries problems w...

In this paper, the variational iteration method (VIM) is used to solve a class of singular boundary value problems. Three numerical examples are selected to illustrate the effectiveness and simplicity of the method. Numerical solutions obtained by the method are of high accuracy. Numerical results show that the method is a satisfactory method.