Chinese mathematics for nonlinear oscillators

Abstract

Ancient Chinese mathematicians made dramatic progress toward answering one of the oldest, most fundamental problem of how to solve approximately a real root of a nonlinear algebra equation in about 2nd century BC. The idea was further extended to nonlinear differential equations by J. H. He in 2002. In this paper, J. H. He's frequency-amplitude formation is used to find periodic solution of a pure nonlinear oscillator (without a linear term). The obtained result is of remarkable accuracy.