Green’s function for the one-dimensional Helmholtz equation: closed-form solution from its Fourier sine series

Detalhes bibliográficos
Autor(a) principal: Castro, Antonio S. De [UNESP]
Data de Publicação: 2021
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1590/1806-9126-RBEF-2021-0068
http://hdl.handle.net/11449/211902
Resumo: It is presented a way to obtain the closed form for Green’s function related to the nonhomogeneous one-dimensional Helmholtz equation with homogeneous Dirichlet conditions on the boundary of the domain from its Fourier sine series representation. A closed form for the sum of the series ∑k=1∞sin⁡k⁢x⁢sin⁡k⁢y/(k2-α2) is found in the process.
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spelling Green’s function for the one-dimensional Helmholtz equation: closed-form solution from its Fourier sine seriesGreen’s function methodNonhomogeneous Helmholtz equationHomogeneous Dirichlet conditions.It is presented a way to obtain the closed form for Green’s function related to the nonhomogeneous one-dimensional Helmholtz equation with homogeneous Dirichlet conditions on the boundary of the domain from its Fourier sine series representation. A closed form for the sum of the series ∑k=1∞sin⁡k⁢x⁢sin⁡k⁢y/(k2-α2) is found in the process.Universidade Estadual Paulista “Júlio de Mesquita Filho”, Departamento de FísicaUniversidade Estadual Paulista “Júlio de Mesquita Filho”, Departamento de FísicaSociedade Brasileira de FísicaUniversidade Estadual Paulista (Unesp)Castro, Antonio S. De [UNESP]2021-07-14T10:31:21Z2021-07-14T10:31:21Z2021-04-16info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article-application/pdfhttp://dx.doi.org/10.1590/1806-9126-RBEF-2021-0068Revista Brasileira de Ensino de Física. Sociedade Brasileira de Física, v. 43, p. -, 2021.1806-11171806-9126http://hdl.handle.net/11449/21190210.1590/1806-9126-RBEF-2021-0068S1806-11172021000100101S1806-11172021000100101.pdfSciELOreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengRevista Brasileira de Ensino de Físicainfo:eu-repo/semantics/openAccess2024-01-16T06:26:13Zoai:repositorio.unesp.br:11449/211902Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T23:07:45.503989Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Green’s function for the one-dimensional Helmholtz equation: closed-form solution from its Fourier sine series
title Green’s function for the one-dimensional Helmholtz equation: closed-form solution from its Fourier sine series
spellingShingle Green’s function for the one-dimensional Helmholtz equation: closed-form solution from its Fourier sine series
Castro, Antonio S. De [UNESP]
Green’s function method
Nonhomogeneous Helmholtz equation
Homogeneous Dirichlet conditions.
title_short Green’s function for the one-dimensional Helmholtz equation: closed-form solution from its Fourier sine series
title_full Green’s function for the one-dimensional Helmholtz equation: closed-form solution from its Fourier sine series
title_fullStr Green’s function for the one-dimensional Helmholtz equation: closed-form solution from its Fourier sine series
title_full_unstemmed Green’s function for the one-dimensional Helmholtz equation: closed-form solution from its Fourier sine series
title_sort Green’s function for the one-dimensional Helmholtz equation: closed-form solution from its Fourier sine series
author Castro, Antonio S. De [UNESP]
author_facet Castro, Antonio S. De [UNESP]
author_role author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (Unesp)
dc.contributor.author.fl_str_mv Castro, Antonio S. De [UNESP]
dc.subject.por.fl_str_mv Green’s function method
Nonhomogeneous Helmholtz equation
Homogeneous Dirichlet conditions.
topic Green’s function method
Nonhomogeneous Helmholtz equation
Homogeneous Dirichlet conditions.
description It is presented a way to obtain the closed form for Green’s function related to the nonhomogeneous one-dimensional Helmholtz equation with homogeneous Dirichlet conditions on the boundary of the domain from its Fourier sine series representation. A closed form for the sum of the series ∑k=1∞sin⁡k⁢x⁢sin⁡k⁢y/(k2-α2) is found in the process.
publishDate 2021
dc.date.none.fl_str_mv 2021-07-14T10:31:21Z
2021-07-14T10:31:21Z
2021-04-16
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.1590/1806-9126-RBEF-2021-0068
Revista Brasileira de Ensino de Física. Sociedade Brasileira de Física, v. 43, p. -, 2021.
1806-1117
1806-9126
http://hdl.handle.net/11449/211902
10.1590/1806-9126-RBEF-2021-0068
S1806-11172021000100101
S1806-11172021000100101.pdf
url http://dx.doi.org/10.1590/1806-9126-RBEF-2021-0068
http://hdl.handle.net/11449/211902
identifier_str_mv Revista Brasileira de Ensino de Física. Sociedade Brasileira de Física, v. 43, p. -, 2021.
1806-1117
1806-9126
10.1590/1806-9126-RBEF-2021-0068
S1806-11172021000100101
S1806-11172021000100101.pdf
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Revista Brasileira de Ensino de Física
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv -
application/pdf
dc.publisher.none.fl_str_mv Sociedade Brasileira de Física
publisher.none.fl_str_mv Sociedade Brasileira de Física
dc.source.none.fl_str_mv SciELO
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
_version_ 1808129491736723456

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