Nonlinear oscillators via \v{C}eby\v{s}\"ev quintic approximations

TL;DR

This paper investigates nonlinear oscillators described by differential equations, focusing on their approximation using Chebyshev quintic polynomials, with applications in relativistic and non-relativistic physical models.

Contribution

It introduces a novel approach to approximate complex nonlinear oscillators using Chebyshev quintic polynomials, extending analysis to relativistic and non-relativistic systems.

Findings

Effective approximation of nonlinear oscillators with Chebyshev quintic polynomials

Application to relativistic and non-relativistic physical models

Enhanced understanding of oscillator dynamics through polynomial methods

Abstract

Aim of this work is the study of differential equations governing non--dissipative non--linear oscillators; these arise in different physical models such as the treatment of relativistic oscillators, up to generalizations to Duffing's relativistic oscillators and in non--relativistic models which deals with cables with an attached midpoint mass, or some harmonic Duffing oscillators.