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

TL;DR

This paper applies the Improved Amplitude-Frequency Formulation (IAFF) to solve strongly nonlinear oscillators, demonstrating high accuracy and simplicity compared to traditional methods like HBM and Exact solutions.

Contribution

The paper introduces and validates the IAFF method for accurately solving strongly nonlinear oscillators, including fractional differential equations, with high efficiency.

Findings

IAFF provides highly accurate approximate solutions.

Solutions are uniformly valid across the entire domain.

Method outperforms traditional approaches like HBM and Exact solutions.

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.