An Accurate Method for Solving the Undamped Duffing Equation with Cubic Nonlinearity

Abstract

In this paper, we study the strongly nonlinear undamped duffing equation for undamped oscillators. We present the physical and the mathematical model of nonlinear Duffing equation for undamped oscillators. The reproducing kernal Hilbert space method (RKHSM) is employed to compute an approximation to the solution of this problem. The validity of the RKHSM is ascertained by comparing our results with numerical results and other methods in the literature. The results reveal that the proposed analytical method can achieve excellent results in predicting the solutions of such problems. The existences of the solution is proved. In addition, the uniformly convergent of the proposed method is investigated.

Keywords Duffing equation, Nonlinear boundary value problem, Reproducing kernel Hilbert space method