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This paper has been retracted as it was found to contain a substantial amount of material, without referencing, from the following published articles: “On the rational second kind Chebyshev pseudospectral method for the solution of the Thomas–Fermi equation over an infinite interval,” published in Journal of Computational and Applied Mathematics (Volume 257, February 2014, Pages 79–85) and “Rational Chebyshev pseudospectral approach for solving Thomas–Fermi equation,” Physics Letters A (Volume 373, Issue 2, 5 January 2009, Pages 210–213).

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  1. M. Tavassoli Kajani, A. Kılıçman, and M. Maleki, “The rational third-kind Chebyshev pseudospectral method for the solution of the Thomas-Fermi equation over infinite interval,” Mathematical Problems in Engineering, vol. 2013, Article ID 537810, 6 pages, 2013.
Mathematical Problems in Engineering
Volume 2013, Article ID 537810, 6 pages
Research Article

The Rational Third-Kind Chebyshev Pseudospectral Method for the Solution of the Thomas-Fermi Equation over Infinite Interval

1Department of Mathematics, Khorasgan Branch, Islamic Azad University, Isfahan 81595-158, Iran
2Department of Mathematics, University Putra Malaysia, (UPM), Serdang, 43400 Selangor, Malaysia
3Department of Mathematics, Mobarakeh Branch, Islamic Azad University, Isfahan, Iran

Received 12 January 2013; Revised 14 May 2013; Accepted 29 May 2013

Academic Editor: Mufid Abudiab

Copyright © 2013 Majid Tavassoli Kajani et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We propose a pseudospectral method for solving the Thomas-Fermi equation which is a nonlinear ordinary differential equation on semi-infinite interval. This approach is based on the rational third-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. Comparison with some numerical solutions shows that the present solution is highly accurate.