Variational iteration method with an auxiliary parameter for solving wave-like and heat-like equations in large domains

The present study is an attempt to obtain solutions of wave-like and heat-like equations with high-dimensional in large domains through the well-known variational iteration method (VIM) which is coupled with an auxiliary parameter. The convergence of the proposed method, namely variational iteration method with an auxiliary parameter, is under investigation. In addition, four examples are provided to elucidate the solution procedure and to optimally choose the auxiliary parameter. Comparing the results of the standard variational iteration method, the auxiliary parameter proves very effective in controlling the convergence region of approximate solution.