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A comparison between pre-Newton and post-Newton approaches for solving a physical singular second-order boundary problem in the semi-infinite interval

    Authors

    • Amir Hosein Hadian Rasanan 1
    • Mehran Nikarya 2
    • Mohammad Mahdi Moayeri 3
    • Arman Bahramnezhad 4

    1 School of Computer Science, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran

    2 Department of Electrical Engineering and Information Technology, Iranian Research Organization for Science and Technology (IROST), Tehran, Iran

    3 Department of Computer and Data Sciences, Shahid Beheshti University, Tehran, Iran.

    4 Department of Computer and Data Sciences, Shahid Beheshti University, Tehran, Iran

,

Document Type : Regular paper

10.52547/CMCMA.1.1.116
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Abstract

In this paper, two numerical approaches based on the Newton iteration method with spectral algorithms are introduced to solve the Thomas-Fermi equation. That Thomas-Fermi equation is a nonlinear singular ordinary differential equation (ODE) with a boundary condition in infinite. In these schemes, the Newton method is combined with a spectral method where in one of those, by the Newton method we convert nonlinear ODE to a sequence of linear ODE and then, solve them using the spectral method. In another one, by the spectral method, the nonlinear ODE is converted to a system of nonlinear algebraic equations, then, this system is solved by the Newton method. In both approaches, the spectral method is based on the fractional order of rational Gegenbauer functions. Finally, the obtained results of the two introduced schemes are compared to each other in accuracy, runtime, and iteration number. Numerical experiments are presented showing that our methods are as accurate as the best results obtained until now.

Keywords

  • Pre-Newton method
  • Post-Newton method
  • Fractional order of rational Gegenbauer functions
  • Thomas-Fermi equation
  • Spectral method
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Computational Mathematics and Computer Modeling with Applications (CMCMA)
Volume 1, Issue 1 - Serial Number 1
June 2022
Pages 116-125
Files
  • XML
  • PDF 225.08 K
History
  • Receive Date: 29 October 2022
  • Revise Date: 25 May 2023
  • Accept Date: 24 July 2023
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How to cite
  • RIS
  • EndNote
  • Mendeley
  • BibTeX
  • APA
  • MLA
  • HARVARD
  • CHICAGO
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Statistics
  • Article View: 78
  • PDF Download: 119

APA

Hadian Rasanan, A. H. , Nikarya, M. , Moayeri, M. M. and Bahramnezhad, A. (2022). A comparison between pre-Newton and post-Newton approaches for solving a physical singular second-order boundary problem in the semi-infinite interval. Computational Mathematics and Computer Modeling with Applications (CMCMA), 1(1), 116-125. doi: 10.52547/CMCMA.1.1.116

MLA

Hadian Rasanan, A. H. , , Nikarya, M. , , Moayeri, M. M. , and Bahramnezhad, A. . "A comparison between pre-Newton and post-Newton approaches for solving a physical singular second-order boundary problem in the semi-infinite interval", Computational Mathematics and Computer Modeling with Applications (CMCMA), 1, 1, 2022, 116-125. doi: 10.52547/CMCMA.1.1.116

HARVARD

Hadian Rasanan, A. H., Nikarya, M., Moayeri, M. M., Bahramnezhad, A. (2022). 'A comparison between pre-Newton and post-Newton approaches for solving a physical singular second-order boundary problem in the semi-infinite interval', Computational Mathematics and Computer Modeling with Applications (CMCMA), 1(1), pp. 116-125. doi: 10.52547/CMCMA.1.1.116

CHICAGO

A. H. Hadian Rasanan , M. Nikarya , M. M. Moayeri and A. Bahramnezhad, "A comparison between pre-Newton and post-Newton approaches for solving a physical singular second-order boundary problem in the semi-infinite interval," Computational Mathematics and Computer Modeling with Applications (CMCMA), 1 1 (2022): 116-125, doi: 10.52547/CMCMA.1.1.116

VANCOUVER

Hadian Rasanan, A. H., Nikarya, M., Moayeri, M. M., Bahramnezhad, A. A comparison between pre-Newton and post-Newton approaches for solving a physical singular second-order boundary problem in the semi-infinite interval. Computational Mathematics and Computer Modeling with Applications (CMCMA), 2022; 1(1): 116-125. doi: 10.52547/CMCMA.1.1.116

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