Solution to a Damped Duffing Equation Using He's Frequency Approach

In this paper, we generalize He's frequency approach for solving the damped Duffing equation by introducing a time varying amplitude. We also solve this equation by means of the homotopy method and the Lindstedt–Poincaré method. High accurate formulas for approximating the Jacobi elliptic funct...

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Detalles Bibliográficos
Autores principales: Salas, Alvaro H. S., Altamirano, Gilder-Cieza, Sánchez-Chero, Manuel
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi 2022
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9293578/
https://www.ncbi.nlm.nih.gov/pubmed/35859637
http://dx.doi.org/10.1155/2022/5009722
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author Salas, Alvaro H. S.
Altamirano, Gilder-Cieza
Sánchez-Chero, Manuel
author_facet Salas, Alvaro H. S.
Altamirano, Gilder-Cieza
Sánchez-Chero, Manuel
author_sort Salas, Alvaro H. S.
collection PubMed
description In this paper, we generalize He's frequency approach for solving the damped Duffing equation by introducing a time varying amplitude. We also solve this equation by means of the homotopy method and the Lindstedt–Poincaré method. High accurate formulas for approximating the Jacobi elliptic function cn are formally derived using Chebyshev and Pade approximation techniques.
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spelling pubmed-92935782022-07-19 Solution to a Damped Duffing Equation Using He's Frequency Approach Salas, Alvaro H. S. Altamirano, Gilder-Cieza Sánchez-Chero, Manuel ScientificWorldJournal Research Article In this paper, we generalize He's frequency approach for solving the damped Duffing equation by introducing a time varying amplitude. We also solve this equation by means of the homotopy method and the Lindstedt–Poincaré method. High accurate formulas for approximating the Jacobi elliptic function cn are formally derived using Chebyshev and Pade approximation techniques. Hindawi 2022-07-11 /pmc/articles/PMC9293578/ /pubmed/35859637 http://dx.doi.org/10.1155/2022/5009722 Text en Copyright © 2022 Alvaro H. S. Salas et al. https://creativecommons.org/licenses/by/4.0/This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Salas, Alvaro H. S.
Altamirano, Gilder-Cieza
Sánchez-Chero, Manuel
Solution to a Damped Duffing Equation Using He's Frequency Approach
title Solution to a Damped Duffing Equation Using He's Frequency Approach
title_full Solution to a Damped Duffing Equation Using He's Frequency Approach
title_fullStr Solution to a Damped Duffing Equation Using He's Frequency Approach
title_full_unstemmed Solution to a Damped Duffing Equation Using He's Frequency Approach
title_short Solution to a Damped Duffing Equation Using He's Frequency Approach
title_sort solution to a damped duffing equation using he's frequency approach
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9293578/
https://www.ncbi.nlm.nih.gov/pubmed/35859637
http://dx.doi.org/10.1155/2022/5009722
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