### 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 |
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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 |
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Country | Greece |

City | Rhodes |

Period | 22/9/14 → 28/9/14 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*AIP Conference Proceedings*(Vol. 1648). [850095] 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; Jovanovic, Raka.

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

*AIP Conference Proceedings.*vol. 1648, 850095, American Institute of Physics Inc., International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014, Rhodes, Greece, 22/9/14. https://doi.org/10.1063/1.4913150

}

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

SN - 9780735412873

VL - 1648

BT - AIP Conference Proceedings

PB - American Institute of Physics Inc.

ER -