Numerical analysis and simulation of the oscillatory pendulum through approximation methods for solving nonlinear ordinary differential equations

Marlon Mollinedo Chura R.; Pumacallahui Salcedo E.; Ccama Alejo R.; Gonzalo Copari Romero F.; Eugenia Mancilla Quispe M.; Marina Acero Coaquira L. · Proceedings of the LACCEI international Multi-conference for Engineering, Education and Technology (2026) · DOI: 10.18687/laccei2026.1.1.2278

Resumen

This paper addresses the numerical analysis of the oscillating pendulum model, described by nonlinear ordinary differential equations. It highlights that the numerical integration of such systems constitutes an essential tool to complement the analytical and qualitative analysis of their solutions, and in many cases, the only feasible approach to characterize their dynamic behavior. The main objective is to evaluate and compare the solution of the nonlinear model with that of the linear model for both small and large initial displacements, showing that linearization is only suitable as a local approximation around the stable equilibrium. For large amplitudes, the use of higher-order numerical methods becomes indispensable to preserve the stability and accuracy of the model, as well as to determine the differences between both approaches. Additionally, key aspects such as the propagation and estimation of numerical error and the stability of integration schemes are analyzed. Finally, computational simulations are implemented in Matlab in order to obtain numerical approximations of the solutions and to examine their dynamic behavior.

Instituciones: Universidad Nacional del Altiplano; Universidad Nacional Intercultural de Quillabamba