NUMERICAL ANALYSIS OF THE DUFFING EQUATION: A COMPARATIVE STUDY

This research aims to carry out an exhaustive comparison between the formulation of the finite difference method and the Runge-Kutta method as numerical approaches to determine the solution of the Duffing oscillator. The Duffing oscillator represented by a nonlinear second-order differential equation, exhibits complex and fascinating dynamics that include bifurcations and periodic orbits in specific regions of its parameters. The purpose of this article is to analyze in detail the results obtained by both methods, highlighting the advantages and limitations of each one in terms of precision, stability, and computational efficiency. The findings of this study offer a deeper perspective on the suitability of the finite difference and Runge-Kutta methods for the numerical resolution of problems involving the Duffing oscillator and contribute to the development of more effective numerical tools for the analysis of nonlinear dynamic systems. Keywords: Discretization, Finite Differences, Convergence, The Runge-Kutta Method, The Duffing Equation DOI： https://doi.org/10.35741/issn.0258-2724.58.4.94