Variational Iteration Method for Solving Higher-order Nonlinear Boundary Value Problems Using He's Polynomials

摘要

In this paper, we apply the variational iteration method using He's polynomials (VIMHP) for solving the higher-order boundary value problems. The proposed method is an elegant combination of variational iteration and the homotopy perturbation methods. The suggested algorithm is quite efficient and is practically well suited for use in these problems. The proposed iterative scheme finds the solution without any discritization, linearization or restrictive assumptions. Several examples are given to verify the reliability and efficiency of the method. The fact that the proposed VIMHP solves nonlinear problems without using the Adomian's polynomials can be considered as a clear advantage of this algorithm over the decomposition method.