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

Hamid Badri; Fahhad H. Alharbi; Raka Jovanovic

doi:10.1063/1.4913150

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

Hamid Badri
, Fahhad H. Alharbi
, Raka Jovanovic

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

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 language	English
Title of host publication	Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014
Editors	Theodore E. Simos, Theodore E. Simos, Theodore E. Simos, Charalambos Tsitouras
Publisher	American Institute of Physics Inc.
ISBN (Electronic)	9780735412873
DOIs	https://doi.org/10.1063/1.4913150
State	Published - 10 Mar 2015
Externally published	Yes

Publication series

Name	AIP Conference Proceedings
Volume	1648
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Bibliographical note

Publisher Copyright:
© 2015 AIP Publishing LLC.

Keywords

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

ASJC Scopus subject areas

General Physics and Astronomy

Access to Document

10.1063/1.4913150

Cite this

Badri, H., Alharbi, F. H., & Jovanovic, R. (2015). Self-consistent approach to solving the 1D Thomas-Fermi equation using an exponential basis set. In T. E. Simos, T. E. Simos, T. E. Simos, & C. Tsitouras (Eds.), Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014 Article 850095 (AIP Conference Proceedings; Vol. 1648). American Institute of Physics Inc.. https://doi.org/10.1063/1.4913150

Badri, Hamid ; Alharbi, Fahhad H. ; Jovanovic, Raka. / Self-consistent approach to solving the 1D Thomas-Fermi equation using an exponential basis set. Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014. editor / Theodore E. Simos ; Theodore E. Simos ; Theodore E. Simos ; Charalambos Tsitouras. American Institute of Physics Inc., 2015. (AIP Conference Proceedings).

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

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 Pad{\'e} approximation for solving the one dimensional Thomas-Fermi equation.",

keywords = "Finite elements method, Self-consistent, Semi-infinite domain, Spectral method, Thomas-fermi equation",

author = "Hamid Badri and Alharbi, \{Fahhad H.\} and Raka Jovanovic",

note = "Publisher Copyright: {\textcopyright} 2015 AIP Publishing LLC.",

year = "2015",

month = mar,

day = "10",

doi = "10.1063/1.4913150",

language = "English",

series = "AIP Conference Proceedings",

publisher = "American Institute of Physics Inc.",

editor = "Simos, \{Theodore E.\} and Simos, \{Theodore E.\} and Simos, \{Theodore E.\} and Charalambos Tsitouras",

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Badri, H, Alharbi, FH & Jovanovic, R 2015, Self-consistent approach to solving the 1D Thomas-Fermi equation using an exponential basis set. in TE Simos, TE Simos, TE Simos & C Tsitouras (eds), Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014., 850095, AIP Conference Proceedings, vol. 1648, American Institute of Physics Inc. https://doi.org/10.1063/1.4913150

Self-consistent approach to solving the 1D Thomas-Fermi equation using an exponential basis set. / Badri, Hamid; Alharbi, Fahhad H.; Jovanovic, Raka.
Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014. ed. / Theodore E. Simos; Theodore E. Simos; Theodore E. Simos; Charalambos Tsitouras. American Institute of Physics Inc., 2015. 850095 (AIP Conference Proceedings; Vol. 1648).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Self-consistent approach to solving the 1D Thomas-Fermi equation using an exponential basis set

AU - Badri, Hamid

AU - Alharbi, Fahhad H.

AU - Jovanovic, Raka

PY - 2015/3/10

Y1 - 2015/3/10

N2 - 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.

AB - 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.

KW - Finite elements method

KW - Self-consistent

KW - Semi-infinite domain

KW - Spectral method

KW - Thomas-fermi equation

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DO - 10.1063/1.4913150

M3 - Conference contribution

AN - SCOPUS:84939647846

T3 - AIP Conference Proceedings

BT - Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014

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ER -

Badri H, Alharbi FH, Jovanovic R. Self-consistent approach to solving the 1D Thomas-Fermi equation using an exponential basis set. In Simos TE, Simos TE, Simos TE, Tsitouras C, editors, Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014. American Institute of Physics Inc. 2015. 850095. (AIP Conference Proceedings). doi: 10.1063/1.4913150

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

Abstract

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Keywords

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