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

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

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 / ( k 2 - α 2 ) is found in the process.

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Bibliographic Details
Main Author: Castro,Antonio S. de
Format: Digital revista
Language:English
Published: Sociedade Brasileira de Física 2021
Online Access:http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172021000100101
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spelling oai:scielo:S1806-111720210001001012021-04-14Green’s function for the one-dimensional Helmholtz equation: closed-form solution from its Fourier sine seriesCastro,Antonio S. de Green’s function method Nonhomogeneous Helmholtz equation Homogeneous 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 / ( k 2 - α 2 ) is found in the process.info:eu-repo/semantics/openAccessSociedade Brasileira de FísicaRevista Brasileira de Ensino de Física v.43 20212021-01-01info:eu-repo/semantics/othertext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172021000100101en10.1590/1806-9126-rbef-2021-0068
institution SCIELO
collection OJS
country Brasil
countrycode BR
component Revista
access En linea
databasecode rev-scielo-br
tag revista
region America del Sur
libraryname SciELO
language English
format Digital
author Castro,Antonio S. de
spellingShingle Castro,Antonio S. de
Green’s function for the one-dimensional Helmholtz equation: closed-form solution from its Fourier sine series
author_facet Castro,Antonio S. de
author_sort Castro,Antonio S. de
title Green’s function for the one-dimensional Helmholtz equation: closed-form solution from its Fourier sine series
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
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 / ( k 2 - α 2 ) is found in the process.
publisher Sociedade Brasileira de Física
publishDate 2021
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172021000100101
work_keys_str_mv AT castroantoniosde greensfunctionfortheonedimensionalhelmholtzequationclosedformsolutionfromitsfouriersineseries
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