The variational iteration method is a special case of the homotopy analysis method

In the present paper, we demonstrate that the variational iteration method (and all of its optimal analogues) are specific cases of the more general homotopy analysis method. To do so, we derive the variational iteration method starting with the homotopy analysis method. The optimal variational iteration method, which also appears in the literature, can be described completely within the context of the optimal homotopy analysis method. Alternately, the optimal homotopy analysis method can be used to construct more general iterative methods of the same ilk, which is potentially useful for solving partial differential equations.