Development of a new iterative method and its convergence analysis for nonlinear fourth‐order boundary value problems arising in beam analysis.

[EN]In this study, an effective iterative technique based on Green's function is proposed to solve a nonlinear fourth-order boundary value problem (BVP) with nonlinear boundary conditions, which models an elastic beam. An iterative Green's function approach and a shooting method are integr...

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Autores: Tomar, Saurabh, Singh, Mehakpreet, Ramos Calle, Higinio, Wazwaz, Abdul‐Majid
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2022
País:España
Institución:Universidad de Salamanca (USAL)
Repositorio:GREDOS. Repositorio Institucional de la Universidad de Salamanca
OAI Identifier:oai:gredos.usal.es:10366/156322
Acceso en línea:http://hdl.handle.net/10366/156322
Access Level:acceso abierto
Palabra clave:Convergence analysis
Elastic beam equation
Nonlinear boundary condition
Nonlinear fourth-order BVP
12 Matemáticas
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spelling Development of a new iterative method and its convergence analysis for nonlinear fourth‐order boundary value problems arising in beam analysis.Tomar, SaurabhSingh, MehakpreetRamos Calle, HiginioWazwaz, Abdul‐MajidConvergence analysisElastic beam equationNonlinear boundary conditionNonlinear fourth-order BVP12 Matemáticas[EN]In this study, an effective iterative technique based on Green's function is proposed to solve a nonlinear fourth-order boundary value problem (BVP) with nonlinear boundary conditions, which models an elastic beam. An iterative Green's function approach and a shooting method are integrated in the proposed method. The mathematical derivation is further supported by examining the convergence analysis of the proposed method. The iterative method rapidly generates a convergent series solution to the given problem. The proposed method has many advantages over existing methods: (a) A rapid convergence and (b) the ability to generate a highly accurate series solution with just a few iterations for complex problems arising in elastic beam. To demonstrate the applicability and effectiveness of the proposed method, four numerical examples are tested. The numerical results show that our methodology delivers more efficient results compared to other existing methods.202420242022info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://hdl.handle.net/10366/156322reponame:GREDOS. Repositorio Institucional de la Universidad de Salamancainstname:Universidad de Salamanca (USAL)InglésAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:gredos.usal.es:10366/1563222026-06-07T06:28:51Z
dc.title.none.fl_str_mv Development of a new iterative method and its convergence analysis for nonlinear fourth‐order boundary value problems arising in beam analysis.
title Development of a new iterative method and its convergence analysis for nonlinear fourth‐order boundary value problems arising in beam analysis.
spellingShingle Development of a new iterative method and its convergence analysis for nonlinear fourth‐order boundary value problems arising in beam analysis.
Tomar, Saurabh
Convergence analysis
Elastic beam equation
Nonlinear boundary condition
Nonlinear fourth-order BVP
12 Matemáticas
title_short Development of a new iterative method and its convergence analysis for nonlinear fourth‐order boundary value problems arising in beam analysis.
title_full Development of a new iterative method and its convergence analysis for nonlinear fourth‐order boundary value problems arising in beam analysis.
title_fullStr Development of a new iterative method and its convergence analysis for nonlinear fourth‐order boundary value problems arising in beam analysis.
title_full_unstemmed Development of a new iterative method and its convergence analysis for nonlinear fourth‐order boundary value problems arising in beam analysis.
title_sort Development of a new iterative method and its convergence analysis for nonlinear fourth‐order boundary value problems arising in beam analysis.
dc.creator.none.fl_str_mv Tomar, Saurabh
Singh, Mehakpreet
Ramos Calle, Higinio
Wazwaz, Abdul‐Majid
author Tomar, Saurabh
author_facet Tomar, Saurabh
Singh, Mehakpreet
Ramos Calle, Higinio
Wazwaz, Abdul‐Majid
author_role author
author2 Singh, Mehakpreet
Ramos Calle, Higinio
Wazwaz, Abdul‐Majid
author2_role author
author
author
dc.subject.none.fl_str_mv Convergence analysis
Elastic beam equation
Nonlinear boundary condition
Nonlinear fourth-order BVP
12 Matemáticas
topic Convergence analysis
Elastic beam equation
Nonlinear boundary condition
Nonlinear fourth-order BVP
12 Matemáticas
description [EN]In this study, an effective iterative technique based on Green's function is proposed to solve a nonlinear fourth-order boundary value problem (BVP) with nonlinear boundary conditions, which models an elastic beam. An iterative Green's function approach and a shooting method are integrated in the proposed method. The mathematical derivation is further supported by examining the convergence analysis of the proposed method. The iterative method rapidly generates a convergent series solution to the given problem. The proposed method has many advantages over existing methods: (a) A rapid convergence and (b) the ability to generate a highly accurate series solution with just a few iterations for complex problems arising in elastic beam. To demonstrate the applicability and effectiveness of the proposed method, four numerical examples are tested. The numerical results show that our methodology delivers more efficient results compared to other existing methods.
publishDate 2022
dc.date.none.fl_str_mv 2022
2024
2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10366/156322
url http://hdl.handle.net/10366/156322
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv Attribution-NonCommercial-NoDerivatives 4.0 Internacional
http://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Attribution-NonCommercial-NoDerivatives 4.0 Internacional
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.source.none.fl_str_mv reponame:GREDOS. Repositorio Institucional de la Universidad de Salamanca
instname:Universidad de Salamanca (USAL)
instname_str Universidad de Salamanca (USAL)
reponame_str GREDOS. Repositorio Institucional de la Universidad de Salamanca
collection GREDOS. Repositorio Institucional de la Universidad de Salamanca
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301603

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