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september 2017 New Numerical Solution For Solving Nonlinear Singular Thomas-Fermi Differential Equation
Kourosh Parand, Mehdi Delkhosh
Bull. Belg. Math. Soc. Simon Stevin 24(3): 457-476 (september 2017). DOI: 10.36045/bbms/1506477694


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.


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Kourosh Parand. Mehdi Delkhosh. "New Numerical Solution For Solving Nonlinear Singular Thomas-Fermi Differential Equation." Bull. Belg. Math. Soc. Simon Stevin 24 (3) 457 - 476, september 2017.


Published: september 2017
First available in Project Euclid: 27 September 2017

zbMATH: 1377.65096
MathSciNet: MR3706814
Digital Object Identifier: 10.36045/bbms/1506477694

Primary: 34B16 , 34B40 , 74S25

Keywords: collocation method , Fractional order of the Chebyshev functions , Nonlinear ODE , Semi-infinite domain , Singular points , Thomas-Fermi equation

Rights: Copyright © 2017 The Belgian Mathematical Society


Vol.24 • No. 3 • september 2017
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