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...

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Detalles Bibliográficos
Autores: Sierra-Porta, D., Chirinos, M., Stock, J.
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
Descripción
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.