Enhancing precision in nonlinear oscillator analysis: A comparative study of multiple-scale analysis and strained coordinates

Abstract

This paper presents a comparative study of three prominent analytical techniques. These are multiple-scale analysis, the method of strained coordinates, and the Poincaré-Lindstedt method for analyzing nonlinear oscillators under singular perturbation. Focusing on the undamped Duffing equation as a representative nonlinear system, we investigate the efficacy, accuracy, and limitations of each method. Notably, all three methods were applied to a single Duffing oscillator problem to evaluate varying degrees of accuracy and computational efficiency. The study highlights the importance of selecting the most suitable analytical tool based on the specific characteristics of the nonlinear oscillator and the nature of the singular perturbation. Our findings contribute to the ongoing refinement of analytical approaches in nonlinear dynamics, offering insights to guide researchers and engineers in choosing the most appropriate method for their specific nonlinear oscillator problems.