Bulletin of the Belgian Mathematical Society - Simon Stevin

New Numerical Solution For Solving Nonlinear Singular Thomas-Fermi Differential Equation

Kourosh Parand and Mehdi Delkhosh

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In this paper, the nonlinear singular Thomas-Fermi differential equation on a semi-infinite domain for neutral atoms is solved by using the generalized fractional order of the Chebyshev orthogonal functions (GFCFs) of the first kind. First, this collocation method reduces the solution of this problem to the solution of a system of nonlinear algebraic equations. Second, using solve a system of nonlinear equations, the initial value for the unknown parameter $L$ is calculated, and finally, the value of $L$ to increase the accuracy of the initial slope is improved and the value of $y'(0)=-1.588071022611375312718684509$ is calculated. The comparison with some numerical solutions shows that the present solution is highly accurate.

Article information

Bull. Belg. Math. Soc. Simon Stevin, Volume 24, Number 3 (2017), 457-476.

First available in Project Euclid: 27 September 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34B16: Singular nonlinear boundary value problems 34B40: Boundary value problems on infinite intervals 74S25: Spectral and related methods

Thomas-Fermi equation Collocation method Fractional order of the Chebyshev functions Semi-infinite domain Singular points Nonlinear ODE


Parand, Kourosh; Delkhosh, Mehdi. New Numerical Solution For Solving Nonlinear Singular Thomas-Fermi Differential Equation. Bull. Belg. Math. Soc. Simon Stevin 24 (2017), no. 3, 457--476. doi:10.36045/bbms/1506477694. https://projecteuclid.org/euclid.bbms/1506477694

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