Thomas-Fermi equation

Thomas-Fermi equation

[′täm·əs ′fer·mē i‚kwā·zhən]
(atomic physics)
The differential equation x 1/2(d 2 y / dx 2)= y 3/2that arises in calculating the potential in the Thomas-Fermi atom model; the physically meaningful solution satisfies the boundary conditions y (0)=1 and y (∞)=0.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Additionally, an adaptive algorithm for the Thomas-Fermi equation by means of the moving mesh finite element method has been developed [31].
An adaptive algorithm for the Thomas-Fermi equation. Numerical Algorithms, 59(3):359-372, 2012.
Numerical Solution of Falkner-Skan Equation by Iterative Transformation Method
Also, it is tried that a history for Thomas-Fermi equation is provided.
In this paper, it is attempted to introduce a Spectral method based on the generalized fractional order of the Chebyshev functions for solving Thomas-Fermi equation.
The nonlinear singular Thomas-Fermi equation is defined as [24, 25, 26]:
New Numerical Solution For Solving Nonlinear Singular Thomas-Fermi Differential Equation
Pirkhedri, "The sinc-collocation method for solving the Thomas-Fermi equation," Journal of Computational and Applied Mathematics, vol.
Numerical algorithm based on Haar-Sinc collocation method for solving the hyperbolic PDEs
The corresponding homogeneous Thomas-Fermi equation is
Thomas-Fermi Equation in the Presence of Minimal Length
Now, the Thomas-Fermi equation ([[nabla].sup.2] - [[lambda].sup.2])U(r) = 0 in this case transforms to the following equation:
Thomas-Fermi model in the presence of natural cutoffs
While the use of only real coefficients is less robust and cannot easily be applied to multimodal functions, it is still suitable for the Thomas-Fermi equation. On the other hand due to it simpler form it has some specific properties.
In this paper, a new approach for solving the Thomas-Fermi equation using spectral methods has been presented.
Spectral method for solving the nonlinear Thomas-Fermi equation based on exponential functions
Adomian, "Solution of the Thomas-Fermi equation," Applied Mathematics Letters, vol.
Constructing uniform approximate analytical solutions for the blasius problem
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