The method of multiple scales applied to a model of the regularly perturbed linear harmonic oscillator

Authors

  • Douglas Machado da Silva Universidade Federal de Pelotas
  • Leslie D. Pérez-Fernández
  • Alexandre Molter
  • Julián Bravo Castillero

DOI:

https://doi.org/10.14808/sci.plena.2023.119908

Keywords:

linear harmonic oscillator, regular perturbation, multiple scales method

Abstract

Perturbation methods are intended to obtain an approximate solution to problems involving a small parameter . This is attained by decomposing the original problem into a recursive sequence of simpler problems, from which a formal asymptotic solution (FAS) of the problem is constructed. However, there are problems for which traditional perturbation theory methods do not provide satisfactory results. This fact is illustrated here for the regularly perturbed linear harmonic oscillator problem. For this problem, as an alternative approach, the method of multiple scales is employed here to construct a FAS that is a good approximation of the exact solution.

Downloads

Published

2023-12-14

How to Cite

Machado da Silva, D., Pérez-Fernández, L. D., Molter, A., & Bravo Castillero, J. . (2023). The method of multiple scales applied to a model of the regularly perturbed linear harmonic oscillator. Scientia Plena, 19(11). https://doi.org/10.14808/sci.plena.2023.119908

Issue

Vol. 19 No. 11 (2023): Novembro/November 2023

Section

ENMC/ECTM/MCSul/SEMENGO

License

Copyright (c) 2023 Douglas Machado da Silva, Leslie D. Pérez-Fernández, Alexandre Molter, Julián Bravo Castillero

Creative Commons License

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

Authors who publish with this journal agree to the following terms:

  1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work