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The main aim of this article is to use a new and simple algorithm namely the modified variational iteration algorithm-II (MVIA-II) to obtain numerical solutions of different types of fifth-order Korteweg-de Vries (KdV) equations. In order to assess the precision, stability and accuracy of the solutions, five test problems are offered for different types of fifth-order KdV equations. Numerical results are compared with the Adomian decomposition method, Laplace decomposition method, modified Adomian decomposition method and the homotopy perturbation transform method, which reveals that the MVIA-II exceptionally productive, computationally attractive and has more accuracy than the others.

This paper deals with the determination of approximate solutions for a model of column buckling using two efficient and powerful methods called He's variational approach and variational iteration algorithm-II. These methods are used to find analytical approximate solution of nonlinear dynamic equation of a model for the column buckling. First and second order approximate solutions of the equation of the system are achieved. To validate the solutions, the analytical results have been compared with those resulted from Runge-Kutta 4th order method. A good agreement of the approximate frequencies and periodic solutions with the numerical results and the exact solution shows that the present methods can be easily extended to other nonlinear oscillation problems in engineering. The accuracy and convenience of the proposed methods are also revealed in comparisons with the other solution techniques. [ABSTRACT FROM AUTHOR]

Abstract: In this paper the problem of the porous slider where the fluid is injected through the porous bottom is considered. The similarity transformation reduces the governing equations into coupled nonlinear ordinary differential equations. The resulting equations are solved by using He’s variational iteration algorithm-II. The resulting series solution contains the well known Reynolds number. The influence of the Reynolds number on the velocity field has been discussed graphically. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to employ an analytical approach to a two-dimensional viscous flow with a shrinking sheet. A comparative study of the variational iteration algorithm-II (VIM-II) and the Adomian decomposition method (ADM) are discussed. Both approaches have been applied to obtain the solution of a two-dimensional viscous flow due to a shrinking sheet. This study outlines the significant features of the two methods. Comparison is made with the ADM to highlight the significant features of the VIM-II and its capability of handling completely integrable equations. Through careful investigation of the iteration formulas of the earlier variational iteration algorithm (VIM), we find unnecessary repeated calculations in each iteration. To overcome this shortcoming, we suggest the VIM-II, which has advantages over other iteration formulas, such as the VIM, and the ADM. Further iterations can produce more accurate results and decrease the error. [ABSTRACT FROM AUTHOR]