Residual calculation in He's frequency-amplitude formulation

He's frequency-amplitude formulation and its modifications mainly depend upon the residual calculation. A suitable choice of a residual leads to an ideal result. This paper discusses some effective methods for the residual calculation, and a modification with a free parameter is suggested to effectively estimate the frequency of a nonlinear oscillator. Furthermore, an energy-based residual calculation is also suggested, which is deduced from a variational principle.

Automated summary

The frequency-amplitude formulation and its modifications heavily rely on residual calculations in this paper. The choice of a suitable residual is crucial for obtaining ideal results. Effective methods for residual calculation are discussed, along with a modification using a free parameter for frequency estimation of a nonlinear oscillator. Additionally, an energy-based residual calculation derived from a variational principle is suggested.