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 | AIP Conference Proceedings |
| Publisher | American Institute of Physics Inc. |
| Volume | 1648 |
| ISBN (Print) | 9780735412873 |
| DOIs | |
| Publication status | Published - 10 Mar 2015 |
| Event | International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014 - Rhodes, Greece Duration: 22 Sep 2014 → 28 Sep 2014 |
Other
| Other | International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014 |
|---|---|
| Country | Greece |
| City | Rhodes |
| Period | 22/9/14 → 28/9/14 |
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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
Self-consistent approach to solving the 1D Thomas-Fermi equation using an exponential basis set. / Badri, Hamid; Alharbi, Fahhad; Jovanovic, Raka.
AIP Conference Proceedings. Vol. 1648 American Institute of Physics Inc., 2015. 850095.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Self-consistent approach to solving the 1D Thomas-Fermi equation using an exponential basis set
AU - Badri, Hamid
AU - Alharbi, Fahhad
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
UR - http://www.scopus.com/inward/record.url?scp=84939647846&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84939647846&partnerID=8YFLogxK
U2 - 10.1063/1.4913150
DO - 10.1063/1.4913150
M3 - Conference contribution
AN - SCOPUS:84939647846
SN - 9780735412873
VL - 1648
BT - AIP Conference Proceedings
PB - American Institute of Physics Inc.
ER -