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The Galerkin Method for Solving Strongly Nonlinear Oscillators

In this paper, we make use of the Galerkin method for solving nonlinear second-order ODEs that are related to some strongly nonlinear oscillators arising in physics and engineering. We derive the iterative schemes for finding the coefficients that appear in the linear Galerkin hat combination in the...

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Autor principal: Salas, Alvaro H. S.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9473878/
https://www.ncbi.nlm.nih.gov/pubmed/36118289
http://dx.doi.org/10.1155/2022/8141227
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author Salas, Alvaro H. S.
author_facet Salas, Alvaro H. S.
author_sort Salas, Alvaro H. S.
collection PubMed
description In this paper, we make use of the Galerkin method for solving nonlinear second-order ODEs that are related to some strongly nonlinear oscillators arising in physics and engineering. We derive the iterative schemes for finding the coefficients that appear in the linear Galerkin hat combination in the ansatz form solution. These coefficients may be found iteratively by solving either a quadratic or a higher degree algebraic equation. Examples are presented to illustrate the obtained results. Some exact solutions are given, and they are compared with both the Runge–Kutta numerical solution and the solution obtained using the Galerkin finite element method.
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spelling pubmed-94738782022-09-15 The Galerkin Method for Solving Strongly Nonlinear Oscillators Salas, Alvaro H. S. ScientificWorldJournal Research Article In this paper, we make use of the Galerkin method for solving nonlinear second-order ODEs that are related to some strongly nonlinear oscillators arising in physics and engineering. We derive the iterative schemes for finding the coefficients that appear in the linear Galerkin hat combination in the ansatz form solution. These coefficients may be found iteratively by solving either a quadratic or a higher degree algebraic equation. Examples are presented to illustrate the obtained results. Some exact solutions are given, and they are compared with both the Runge–Kutta numerical solution and the solution obtained using the Galerkin finite element method. Hindawi 2022-09-07 /pmc/articles/PMC9473878/ /pubmed/36118289 http://dx.doi.org/10.1155/2022/8141227 Text en Copyright © 2022 Alvaro H. S. Salas. 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.
The Galerkin Method for Solving Strongly Nonlinear Oscillators
title The Galerkin Method for Solving Strongly Nonlinear Oscillators
title_full The Galerkin Method for Solving Strongly Nonlinear Oscillators
title_fullStr The Galerkin Method for Solving Strongly Nonlinear Oscillators
title_full_unstemmed The Galerkin Method for Solving Strongly Nonlinear Oscillators
title_short The Galerkin Method for Solving Strongly Nonlinear Oscillators
title_sort galerkin method for solving strongly nonlinear oscillators
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9473878/
https://www.ncbi.nlm.nih.gov/pubmed/36118289
http://dx.doi.org/10.1155/2022/8141227
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