An open problem on the optimality of an asymptotic solution to Duffing’s nonlinear oscillation problem

• We solve an open problem proposed in the journal SIAM Review.
• The problem is about the optimality of an asymptotic solution.
• We give an affirmative answer to the problem by means of the homotopy analysis method.

Based on the renormalization group method, Kirkinis (2012) [8] obtained an asymptotic solution to Duffing’s nonlinear oscillation problem. Kirkinis then asked if the asymptotic solution is optimal. In this paper, an affirmative answer to the open problem is given by means of the homotopy analysis method.