Bulletin of the Belgian Mathematical Society - Simon Stevin

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

Abstract

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

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

Dates
First available in Project Euclid: 27 September 2017

https://projecteuclid.org/euclid.bbms/1506477694

Digital Object Identifier
doi:10.36045/bbms/1506477694

Mathematical Reviews number (MathSciNet)
MR3706814

Zentralblatt MATH identifier
1377.65096

Citation

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