Development of accurate solutions for a classical oscillator

TL;DR

This paper introduces a new analytical method for accurately solving conservative classical oscillators, effective across various nonlinearities, and compares it favorably to the Lindstedt-Poincaré method.

Contribution

The paper presents a novel analytical approach for solving classical oscillators that improves accuracy and applicability over existing methods like Lindstedt-Poincaré.

Findings

Method provides arbitrarily accurate solutions

Effective for small and large nonlinearities

Outperforms Lindstedt-Poincaré method

Abstract

We present a method to obtain arbitrarily accurate solutions for conservative classical oscillators. The method that we propose here works both for small and large nonlinearities and provides simple analytical approximations. A comparison with the standard Lindstedt-Poincar\'e method is presented, from which the advantages of our method are clear.