Abstract
In order to obtain a highly accurate periodic solution for systems based on strongly quadratic nonlinear oscillators, an averaging method, which has been improved through the use of the Jacobian elliptic function, is proposed. In this averaging method, the Jacobian elliptic sine function is incorporated as the generating solution. The stability criterion for the approximate solutions obtained by this method is also presented. The efficiency of the proposed method is illustrated by comparing its computational results with those obtained by the shooting method and the conventional averaging method. It is confirmed that the proposed method provides a more accurate solution than the conventional averaging method, which uses a trigonometric function as the generating solution.
