Self-consistent approach to solving the 1D Thomas-Fermi equation using an exponential basis set

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Abstract

In this paper we focus on calculating an approximate solution to the one dimensional Thomas-Fermi equation in the form of an expansion using exponential basis functions. We use a self-consistent approach for finding the expansion coefficients. In practice this results in an iterative algorithm. In this way, the problem of solving a system of nonlinear equations, which is common for other similar methods for finding approximate solutions for the equation of interest, is avoided. The evaluation of this approach has been performed in two directions. First, to see the effect of using the exponential basis set, we compare the quality of found approximate solutions using the proposed algorithm with an analog self-consistent approach based on finite elements. A comparison is also conducted with the use of Padé approximation for solving the one dimensional Thomas-Fermi equation.

Original languageEnglish
Title of host publicationAIP Conference Proceedings
PublisherAmerican Institute of Physics Inc.
Volume1648
ISBN (Print)9780735412873
DOIs
Publication statusPublished - 10 Mar 2015
EventInternational Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014 - Rhodes, Greece
Duration: 22 Sep 201428 Sep 2014

Other

OtherInternational Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014
CountryGreece
CityRhodes
Period22/9/1428/9/14

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Keywords

  • Finite elements method
  • Self-consistent
  • Semi-infinite domain
  • Spectral method
  • Thomas-fermi equation

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Badri, H., Alharbi, F., & Jovanovic, R. (2015). Self-consistent approach to solving the 1D Thomas-Fermi equation using an exponential basis set. In AIP Conference Proceedings (Vol. 1648). [850095] American Institute of Physics Inc.. https://doi.org/10.1063/1.4913150