Comments on “A one-step optimal homotopy analysis method for nonlinear differential equations”

The above mentioned paper contains some fundamental mistakes and misinterpretations along with a false conclusion. Applying the optimal homotopy asymptotic method (OHAM) in an incorrect manner, Niu and Wang have drawn the false conclusion that this approach is not efficient in practice because it is time-consuming for high-order of approximation. We emphasized the presence of some evident mistakes and misinterpretations in their paper and we proved that OHAM is very efficient in practice since we solved all three examples analyzed by Niu and Wang using only the first-order of approximation, which yields accurate results. We demonstrate that OHAM does not need high-orders of approximation as Niu and Wang suggests and we show that the main strength of OHAM is its rapid convergence, contradicting Niu and Wang’s assumption.