Comparison of solutions to the Thomas-Fermi equation by a direct method and variational calculus

• D. Sierra-Porta ^[1] ; M. Chirinos ^[2] ; J. Stock ^[2]
  1. [1] Universidad Industrial de Santander

     Universidad Industrial de Santander

     Colombia

     
  2. [2] La Universidad del Zulia

     La Universidad del Zulia

     Venezuela

     
• Localización: Revista Mexicana de Física, ISSN-e 0035-001X, Vol. 63, Nº. 4, 2017, págs. 333-338
• Idioma: español
• Enlaces
  • Texto completo
• Resumen

  • 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.