Hossein Ghaneai - Department of Computer Engineering, Meybod University, Meybod, Iran
Mohammad Mirabi - Department of Industrial Engineering, Meybod University, Meybod, Iran
Reza Rashidi - Department of MechanicalEngineering, Meybod University, Meybod, Iran

The value of an auxiliary parameter incorporated into the well-known variational iteration method (VIM) to obtain solutions of wave equations in unbounded domains is discussed in this article. The suggested method, namely the optimal variational iteration method, is investigated for convergence. Furthermore, the proposed method is tested on one-dimensional and two-dimensional wave equations in unbounded domains in order to better understand the solution mechanism and choose the best auxiliary parameter.Comparisons with results from the standard variational iteration procedure demonstrate that the auxiliary parameter is very useful in tracking the convergence field of the approximate solution.

Wave equations, Unbounded domaines, Variational iteration method, Optimal variational iteration method, Auxiliary parameter, Hermite-Gauss quadrature.