On the rational second kind Chebyshev pseudospectral method for the solution of the Thomas-Fermi equation over an infinite interval

A. Kiliçman; Ishak Hashim; M. Tavassoli Kajani; Mohammad Maleki

doi:10.1016/j.cam.2013.07.050

On the rational second kind Chebyshev pseudospectral method for the solution of the Thomas-Fermi equation over an infinite interval

A. Kiliçman
, Ishak Hashim
, M. Tavassoli Kajani
, Mohammad Maleki

Universiti Putra Malaysia
Universiti Kebangsaan Malaysia
Islamic Azad University

Research output: Contribution to journal › Article › peer-review

25 Scopus citations

Abstract

In this paper, we propose a pseudospectral method for solving the Thomas-Fermi equation which is a nonlinear singular ordinary differential equation on a semi-infinite interval. This approach is based on the rational second kind Chebyshev pseudospectral method that is indeed a combination of tau and collocation methods. This method reduces the solution of this problem to the solution of a system of algebraic equations. The slope at origin is provided with high accuracy. Comparison with some numerical solutions shows that the present solution is effective and highly accurate.

Original language	English
Pages (from-to)	79-85
Number of pages	7
Journal	Journal of Computational and Applied Mathematics
Volume	257
DOIs	https://doi.org/10.1016/j.cam.2013.07.050
State	Published - 2014
Externally published	Yes

Keywords

Chebyshev functions
ODE
Pseudospectral method
Rational second kind
Semi-infinite interval
Singular
Thomas-Fermi equation

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10.1016/j.cam.2013.07.050

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title = "On the rational second kind Chebyshev pseudospectral method for the solution of the Thomas-Fermi equation over an infinite interval",

abstract = "In this paper, we propose a pseudospectral method for solving the Thomas-Fermi equation which is a nonlinear singular ordinary differential equation on a semi-infinite interval. This approach is based on the rational second kind Chebyshev pseudospectral method that is indeed a combination of tau and collocation methods. This method reduces the solution of this problem to the solution of a system of algebraic equations. The slope at origin is provided with high accuracy. Comparison with some numerical solutions shows that the present solution is effective and highly accurate.",

keywords = "Chebyshev functions, ODE, Pseudospectral method, Rational second kind, Semi-infinite interval, Singular, Thomas-Fermi equation",

author = "A. Kili{\c c}man and Ishak Hashim and \{Tavassoli Kajani\}, M. and Mohammad Maleki",

year = "2014",

doi = "10.1016/j.cam.2013.07.050",

language = "English",

volume = "257",

pages = "79--85",

journal = "Journal of Computational and Applied Mathematics",

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T1 - On the rational second kind Chebyshev pseudospectral method for the solution of the Thomas-Fermi equation over an infinite interval

AU - Kiliçman, A.

AU - Hashim, Ishak

AU - Tavassoli Kajani, M.

AU - Maleki, Mohammad

PY - 2014

Y1 - 2014

N2 - In this paper, we propose a pseudospectral method for solving the Thomas-Fermi equation which is a nonlinear singular ordinary differential equation on a semi-infinite interval. This approach is based on the rational second kind Chebyshev pseudospectral method that is indeed a combination of tau and collocation methods. This method reduces the solution of this problem to the solution of a system of algebraic equations. The slope at origin is provided with high accuracy. Comparison with some numerical solutions shows that the present solution is effective and highly accurate.

AB - In this paper, we propose a pseudospectral method for solving the Thomas-Fermi equation which is a nonlinear singular ordinary differential equation on a semi-infinite interval. This approach is based on the rational second kind Chebyshev pseudospectral method that is indeed a combination of tau and collocation methods. This method reduces the solution of this problem to the solution of a system of algebraic equations. The slope at origin is provided with high accuracy. Comparison with some numerical solutions shows that the present solution is effective and highly accurate.

KW - Chebyshev functions

KW - ODE

KW - Pseudospectral method

KW - Rational second kind

KW - Semi-infinite interval

KW - Singular

KW - Thomas-Fermi equation

UR - https://www.scopus.com/pages/publications/84884266481

U2 - 10.1016/j.cam.2013.07.050

DO - 10.1016/j.cam.2013.07.050

M3 - Article

AN - SCOPUS:84884266481

SN - 0377-0427

VL - 257

SP - 79

EP - 85

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

ER -

On the rational second kind Chebyshev pseudospectral method for the solution of the Thomas-Fermi equation over an infinite interval

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Keywords

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