Comparison of alternative improved perturbative methods for nonlinear oscillations

TL;DR

This paper compares two perturbative methods for calculating the period of nonlinear oscillators, demonstrating that each method performs best for specific types of models like anharmonic oscillators and the Van der Pol equation.

Contribution

It introduces and compares two alternative perturbation techniques based on Lindstedt--Poincaré for nonlinear oscillations, highlighting their respective advantages.

Findings

Each method is optimal for different nonlinear models.

The approaches provide accurate period calculations for anharmonic oscillators.

One method outperforms the other for the Van der Pol oscillator.

Abstract

We discuss and compare two alternative perturbation approaches for the calculation of the period of nonlinear systems based on the Lindstedt--Poincar\'{e} technique. As illustrative examples we choose one--dimensional anharmonic oscillators and the Van der Pol equation. Our results show that each approach is better for just one type of model considered here.