Article Published In Vol.1 (Nov-Dec-2013)

Application of Homotopy Perturbation and Reconstruction of Variational Iteration Methods for Harry Dym Equation and Compared with Exact Solution

Author : Delara soltani, Majid Akbarzadeh Khorshidi

In this paper, an approximate analytical solution of Harry Dym equation is obtained by using reconstruction of variational iteration method (RVIM) and homotopy perturbation method (HPM), RVIM is based on use of Lagrange multipliers for identification of optimal values of parameters in a function by using Laplace transform. The excellent accuracy of the obtained results is demonstrated by comparing them with available analytical and numerical results in the literature. Both of methods have considerable error for large values of t and x, but the Harry Dym equation is applicable for a limited range of t and x. As a result, RVIM is better than HPM especially for larger values of time parameter and the obtained results are close to exact results. The obtained results expose effectiveness and capability of this method to solve the nonlinear systems in mechanics, analytically.

Keywords: Harry Dym equation, Homotopy Perturbation Method, Reconstruction Variational Iteration Method, nonlinear equation, approximate solution.