Bulletin of the Belgian Mathematical Society - Simon Stevin

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

Kourosh Parand and Mehdi Delkhosh

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1506477694

Mathematical Reviews number (MathSciNet)
MR3706814

Zentralblatt MATH identifier
1377.65096

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

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

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


Export citation