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A novel numerical technique to obtain an accurate solution to the Thomas-Fermi equation

The European Physical Journal Plus volume 131, Article number: 228 (2016) Cite this article

Abstract.

In this paper, a new algorithm based on the fractional order of rational Euler functions (FRE) is introduced to study the Thomas-Fermi (TF) model which is a nonlinear singular ordinary differential equation on a semi-infinite interval. This problem, using the quasilinearization method (QLM), converts to the sequence of linear ordinary differential equations to obtain the solution. For the first time, the rational Euler (RE) and the FRE have been made based on Euler polynomials. In addition, the equation will be solved on a semi-infinite domain without truncating it to a finite domain by taking FRE as basic functions for the collocation method. This method reduces the solution of this problem to the solution of a system of algebraic equations. We demonstrated that the new proposed algorithm is efficient for obtaining the value of \( y'(0)\) , \( y(x)\) and \( y'(x)\) . Comparison with some numerical and analytical solutions shows that the present solution is highly accurate.

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Authors and Affiliations

  1. Department of Computer Sciences, Shahid Beheshti University, G.C., Tehran, Iran

    Kourosh Parand, Hossein Yousefi, Mehdi Delkhosh & Amin Ghaderi

  2. Department of Cognitive Modelling, Institute for Cognitive and Brain Sciences, Shahid Beheshti University, Tehran, Iran

    Kourosh Parand

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  1. Kourosh Parand
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Parand, K., Yousefi, H., Delkhosh, M. et al. A novel numerical technique to obtain an accurate solution to the Thomas-Fermi equation. Eur. Phys. J. Plus 131, 228 (2016). https://doi.org/10.1140/epjp/i2016-16228-x

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