He’s frequency–amplitude formulation with average residuals for nonlinear oscillators

In He’s frequency–amplitude formulation, the relationship between frequency and amplitude of a nonlinear oscillator can be obtained through residuals of two trial solutions. Although a high accurate solution can be obtained, this method has some space to be further improved. Here, we show that the calculation of the residuals can be further simplified without loss of accuracy. Duffing oscillator with high nonlinearity is used as an example to show the solution process and accuracy.