Bulletin of the Belgian Mathematical Society - Simon Stevin
- Bull. Belg. Math. Soc. Simon Stevin
- Volume 24, Number 3 (2017), 457-476.
New Numerical Solution For Solving Nonlinear Singular Thomas-Fermi Differential Equation
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.
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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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