scholarly journals Accurate solution of the Thomas–Fermi equation using the fractional order of rational Chebyshev functions

2017 ◽  
Vol 317 ◽  
pp. 624-642 ◽  
Author(s):  
Kourosh Parand ◽  
Mehdi Delkhosh
Keyword(s):  
Fractional Order ◽  
Accurate Solution ◽  
Thomas Fermi ◽  
Rational Chebyshev Functions ◽  
Rational Chebyshev ◽  
Chebyshev Functions

scholarly journals An efficient numerical method for solving nonlinear Thomas-Fermi equation

2018 ◽  
Vol 10 (1) ◽  
pp. 134-151 ◽  
Author(s):  
Kourosh Parand ◽  
Kobra Rabiei ◽  
Mehdi Delkhosh
Keyword(s):  
Collocation Methods ◽  
Arbitrary Parameter ◽  
Algebraic Equations ◽  
Approximation Solution ◽  
Thomas Fermi ◽  
Linear Algebraic Equations ◽  
Rational Chebyshev Functions ◽  
Approximate Amount ◽  
Rational Chebyshev ◽  
Fourier Spectral Methods

Abstract In this paper, the nonlinear Thomas-Fermi equation for neutral atoms by using the fractional order of rational Chebyshev functions of the second kind (FRC2), ${\rm{FU}}_{\rm{n}}^\alpha \left( {{\rm{t}},{\rm{L}}} \right)$ (t, L), on an unbounded domain is solved, where L is an arbitrary parameter. Boyd (Chebyshev and Fourier Spectral Methods, 2ed, 2000) has presented a method for calculating the optimal approximate amount of L and we have used the same method for calculating the amount of L. With the aid of quasilinearization and FRC2 collocation methods, the equation is converted to a sequence of linear algebraic equations. An excellent approximation solution of y(t), y′ (t), and y ′ (0) is obtained.

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