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...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | Portuguese |
| Published: |
Sociedade Brasileira de Física
2021-04-01
|
| Series: | Revista Brasileira de Ensino de Física |
| Subjects: | |
| Online Access: | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172021000100101&tlng=en |
| _version_ | 1818955534418575360 |
|---|---|
| author | Antonio S. de Castro |
| author_facet | Antonio S. de Castro |
| author_sort | Antonio S. de Castro |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-20T10:39:35Z |
| format | Article |
| id | doaj.art-c731143145cd40bd926466c3cea18e1b |
| institution | Directory Open Access Journal |
| issn | 1806-9126 |
| language | Portuguese |
| last_indexed | 2024-12-20T10:39:35Z |
| publishDate | 2021-04-01 |
| publisher | Sociedade Brasileira de Física |
| record_format | Article |
| series | Revista Brasileira de Ensino de Física |
| spelling | doaj.art-c731143145cd40bd926466c3cea18e1b2022-12-21T19:43:34ZporSociedade Brasileira de FísicaRevista Brasileira de Ensino de Física1806-91262021-04-014310.1590/1806-9126-rbef-2021-0068Green’s function for the one-dimensional Helmholtz equation: closed-form solution from its Fourier sine seriesAntonio S. de Castrohttps://orcid.org/0000-0001-8802-8806It 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.http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172021000100101&tlng=enGreen’s function methodNonhomogeneous Helmholtz equationHomogeneous Dirichlet conditions. |
| spellingShingle | Antonio S. de Castro Green’s function for the one-dimensional Helmholtz equation: closed-form solution from its Fourier sine series Revista Brasileira de Ensino de Física Green’s function method Nonhomogeneous Helmholtz equation Homogeneous Dirichlet conditions. |
| title | 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_short | 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 |
| topic | Green’s function method Nonhomogeneous Helmholtz equation Homogeneous Dirichlet conditions. |
| url | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172021000100101&tlng=en |
| work_keys_str_mv | AT antoniosdecastro greensfunctionfortheonedimensionalhelmholtzequationclosedformsolutionfromitsfouriersineseries |