Los  métodos de Numerov y Runge-Kutta-Verner aplicados al movimiento de un sistema mecánico con un grado de libertad

Gustavo J. Bracho Rodríguez

doi:10.48204/j.tecno.v27n1.a6636

Submitted December 27, 2024

Published 2025-01-03

Artículos

Vol. 27 No. 1 (2025): Tecnociencia

Numerov and Runge-Kutta-Verner methods applied to the motion of a mechanical system with one degree of freedom

Gustavo J. Bracho Rodríguez ⁺⁻

DOI https://doi.org/10.48204/j.tecno.v27n1.a6636

PDF (Español (España))

References

DOI: 10.48204/j.tecno.v27n1.a6636

Published: 2025-01-03

How to Cite

Bracho Rodríguez , G. J. (2025) “Numerov and Runge-Kutta-Verner methods applied to the motion of a mechanical system with one degree of freedom”, Tecnociencia, 27(1), pp. 53–69. doi: 10.48204/j.tecno.v27n1.a6636.

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Abstract

This article shows the use of both the Numerov method and the fifth-order Runge-Kutta-Verner method where a comparison is made between the obtained numerical solutions and the corresponding exact solution for a one degree of freedom mass-spring-damper mechanical system experiencing free harmonic damped motion under underdamping and overdamping regimes, respectively. The numerical solutions are obtained by executing source codes written in Python 3. The purpose of the article is to evaluate and contrast the accuracy and computational efficiency of both methods in solving ordinary differential equations (ODEs) that describe the dynamic behavior of a mechanical system. To achieve this, specific examples are presented in which both algorithms are applied to systems with physically admissible initial conditions. The results obtained show that, although both methods provide accurate solutions for the system studied, the Numerov method stands out for its accuracy, while the Runge-Kutta-Verner method presents advantages in terms of greater flexibility and efficiency in problems with greater numerical complexity. The article concludes, among other aspects, the importance of the fact that even though both methods are based on completely different approaches, they present excellent correspondences between the numerical results and the exact solutions between both, despite the fact that their fields of study where they act are completely different.

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