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 ...

We show that the Adomian decomposition method, the time–series expansion, the homotopy–perturbation method, and the variational– iteration method completely fail to provide a reasonable description of the dynamics of the simplest prey–predator system. In is well known that a reasonable description of the dynamics of a nonlinear system by means of a perturbation method is a difficult enterprize ...

In this paper, we introduce a modified variational iteration method for second order initial value problems by transforming the integral of iteration process. The main advantages of this modification are that it can overcome the restriction of the form of nonlinearity term in differential equations and improve the iterative speed of conventional variational iteration method. The method is appli...

In the present paper, a new analytical technique is introduced for obtaining approximate periodic solutions of Helmholtz-Duffing oscillator. Modified Harmonic Balance Method (MHBM) is adopted as the solution method. A classical harmonic balance method does not apply directly for solving Helmholtz-Duffing oscillator. Generally, a set of difficult nonlinear algebraic equations is found when MHBM ...

tension-leg platform (tlp) is a vertically moored floating structure. the platform is permanently mooredby tendons. surge equation of motion of tlp is highly nonlinear because of large displacement and it should be solved with perturbation parameter in time domain. this paper compare the dynamic motion responses of a tlp in regular sea waves obtained by applying three method in time domain usin...

We propose a generalization of the Weierstrass iteration for over-constrained systems of equations and we prove that the proposed method is the Gauss-Newton iteration to find the nearest system which has at least k common roots and which is obtained via a perturbation of prescribed structure. In the univariate case we show the connection of our method to the optimization problem formulated by K...