Analysis of Strongly Non-linear Oscillators by He`s Improved Amplitude-Frequency Formulation

Abstract

In this work, we implement a relatively new analytical technique, the Improved Amplitude-Frequency Formulation (IAFF) method, approach for solving accurate approximate analytical solutions for strong nonlinear oscillators, which may contain high nonlinear terms. This method can be used to obtain analytic and approximate solutions of different types of fractional differential equations applied in engineering mathematics. The solutions obtained are compared with those obtained by the Harmonic balance method (HBM) and Exact method, showing excellent agreement. We find that these attained solutions are not only with high degree of accuracy, but also uniformly valid in the whole solution domain which are so simple-to-do and effective.