An efficient numerical method for solving nonlinear Thomas-Fermi equation

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), FUnα(t,L)${\rm{FU}}_{\rm{n}}^\alpha \left( {{\rm{t}},{\rm{L}}} \right)$ (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.