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

Abstract

In this work, a comprehensive numerical analysis of the oscillating pendulum model is undertaken. The numerical integration of nonlinear ordinary differential equations constitutes an essential complement to the analytical and qualitative study of their solutions and, in numerous instances, represents the only viable approach for obtaining meaningful insight into their dynamical behavior. This study systematically presents and examines the principal numerical integration methods for ordinary differential equations. The primary objective is to evaluate and compare these methods in the context of the oscillating pendulum model, particularly in regimes where closed-form analytical solutions are not attainable. In addition, fundamental issues such as error estimation, convergence, and numerical stability are rigorously addressed. Finally, computational simulations were conducted using MATLAB to illustrate and analyze the resulting numerical solutions.