Accuracy Estimation of the Numerical Solutions for Chaotic Regime of the Pendulum With External and Parametric Excitation

This study involves the development of a framework for checking the accuracy of built‐in algorithms from Mathcad software. The built‐in algorithms used inside Mathcad software include Runge–Kutta method of the fourth order (RK4), Adams method, backward differential formula, AdamsBDF, Radau, Bulstoer, Stiffr, and Stiffb methods. Pendulums have been studied in engineering and science to investigate oscillating motion and vibrating systems. In Physics, pendulums highlight concepts such as wave interference and resonance, making pendulum studies interesting. A pendulum with external and parametric excitation terms is used as a case study for chaotic systems. The numerical results, presented in both tabular and graphical forms, were compared with the Joubert–Greeff method, which was developed using the Duffing equation. Joubert–Greeff method was developed by increasing the order of differential equation.