Comparison of solutions to the Thomas-Fermi equation by a direct method and variational calculus
In this paper we perform a comparison between two solutions of the Thomas-Fermi equation. One of these solutions is the one recently found by Bougoffa (2014) which makes use of a direct method to solve the differential equation. The other solution found uses a variational method. The first method us...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2017 |
| País: | México |
| Institución: | UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO |
| Repositorio: | Revista Mexicana de Física |
| Idioma: | inglés |
| OAI Identifier: | oai:ojs2.rmf.smf.mx:article/351 |
| Acceso en línea: | https://rmf.smf.mx/ojs/index.php/rmf/article/view/351 |
| Access Level: | acceso abierto |
| Palabra clave: | Thomas-Fermi equation approximate solution variational calculus |
| Sumario: | In this paper we perform a comparison between two solutions of the Thomas-Fermi equation. One of these solutions is the one recently found by Bougoffa (2014) which makes use of a direct method to solve the differential equation. The other solution found uses a variational method. The first method uses approximations of the residual conditions after assuming a trial function, inspired by the Sommerfeld solution. Our solution does not require approximations and we found that it reproduces more conveniently the corresponding numerical solution in terms of relative error. |
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