Engineering Transactions, 50, 1-2, pp. 35–42, 2002

Periodic Solutions for a Kind of Nonlinear Oscillations by a New Asymptotic Approach

Ji-Huan He
Shanghai Donghua University
China

This paper proposes a new asymptotic approach to search for the periodic solutions of a kind of nonlinear oscillations. In this method the iteration technique is coupled with the traditional perturbation techniques, yielding a powerful mathematical tool for solving strongly nonlinear equations. Some examples are given to illustrate its effectiveness, convenience and accuracy. Generally, the first iteration leads to a highly accurate approximate solution which is uniformly valid for the whole solution domain. The new asymptotic approach is named the iteration-perturbation method.
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