Contemporary Engineering Sciences, Vol. 11, 2018, no. 52, 2563 - 2570 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ces.2018.86267 Comparative Study of the Use of Numerical Methods in the Solution of Dynamic Mechanical Systems Jorge Duarte 1 , Guillermo E. Valencia 2 and Luis G. Obregón 3 1 Mechanical Eng., Efficient Energy Management Research Group – Kaí Universidad del Atlántico, Carrera 30 Número 8 – 49 Puerto Colombia – Colombia 2 Mechanical Eng., Efficient Energy Management Research Group – Kaí Universidad del Atlántico, Carrera 30 Número 8 – 49 Puerto Colombia – Colombia 3 Sustainable Chemical, and Biochemical Processes Research Group Universidad del Atlántico, Carrera 30 Número 8 – 49 Puerto Colombia – Colombia Copyright © 2018 Jorge Duarte, Guillermo E. Valencia and Luis G. Obregón. This article is distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited. Abstract In the present work, a comparative study of three numerical methods used in the solution of differential equations (Euler, Runge-Kutta and Verlet) was carried out, in order to evaluate the accuracy offered by each of these in the solution of dynamic systems, in addition to other characteristics, particularly the speed of convergence shown for each model, which relates directly with the computational load required for their operation. The methods used for the investigation were compiled in the free computational package Octave, which in turn is a tool with similar characteristics over its paid counterpart (MATLAB®), and applied over a fairly simple dynamic system, which comprises a physical pendulum. The results show that the classic methods (Euler and Runge-Kutta), were able to predict the response of the system accurately, but at a low speed of calculation, while Verlet’s integration method allowed to obtain convergence using a higher time step which implies a faster operation and a better accuracy than the other methods and makes