Study of Duffing oscillator using an improved Lindstedt Poincare method and relevant comparisons

Ramij Ahamed; Subhankar Ray

Study of Duffing oscillator using an improved Lindstedt Poincare method and relevant comparisons

Mathematical Physics 2026-07-16 v1 Classical Physics Computational Physics

Authors: Ramij Ahamed , Subhankar Ray

Abstract

The undamped Duffing oscillator is a nonlinear dynamical system with broad applications in physics, engineering and biological system. We present a comprehensive analysis of this system using the Lindstedt Poincare method (LPM) and its modifications and make comparison with numerical solution obtained using higher order Runge-Kutta. It is also shown the method suggested in this article converges better than the standard LPM and Lindstedt Poincare method with Burton's modification.

Keywords

Duffing oscillator Lindstedt-Poincaré method nonlinear dynamics perturbation methods Runge-Kutta

Cite

@article{arxiv.2607.15233,
  title  = {Study of Duffing oscillator using an improved Lindstedt Poincare method and relevant comparisons},
  author = {Ramij Ahamed and Subhankar Ray},
  journal= {arXiv preprint arXiv:2607.15233},
  year   = {2026}
}