Convergent optimal variational iteration method and applications to heat and fluid flow problems

Purpose – In an earlier paper (Turkyilmazoglu, 2011a), the author introduced a new optimal variational iteration method. The idea was to insert a parameter into the classical variational iteration formula in an aim to prevent divergence or to accelerate the slow convergence property of the classical approach. The purpose of this paper is to approve the superiority of the proposed method over the traditional one on several physical problems treated before by the classical variational iteration method. Design/methodology/approach – A sufficient condition theorem with an upper bound for the error is also presented to further justify the convergence of the new variational iteration method. Findings – The optimal variational iteration method is found to be useful for heat and fluid flow problems. Originality/value – The optimal variational iteration method is shown to be convergent under sufficient conditions. A novel approach to obtain the optimal convergence parameter is introduced.