Approximation Techniques for Non Linear Oscillators

TL;DR

This paper compares approximation methods for nonlinear oscillators, highlighting the reliability of Lindstedt-Poincare perturbation theory for small coupling and cautioning against potential inaccuracies of harmonic balance when expanded perturbatively.

Contribution

It demonstrates the consistent effectiveness of Lindstedt-Poincare perturbation theory and identifies limitations of harmonic balance in certain regimes.

Findings

Lindstedt-Poincare method is reliable for small coupling constants.

Harmonic balance can produce incorrect results when expanded perturbatively.

Perturbation expansion of harmonic balance may lead to inaccuracies.

Abstract

We show that the Lindstedt-Poincare perturbation theory is always a reliable technique in the region of small coupling constant. The harmonic balance result, on the other hand, if expanded in the perturbation parameter may lead to incorrect results.