An effective approach for approximate analytical solutions of the damped Duffing equation

This paper deals with the purely analytic solutions to the damped Duffing equation. It is shown that the employed homotopy method yields uniformly convergent solutions. Optimum values of the convergence control parameter of the computed homotopy series are calculated from the square residual error. The obtained explicit analytical expressions for the solution generate results that compare excellently with the numerically computed ones, which are further confirmed analytically by the absolute error formula.