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

摘要

In this paper, the nonlinear singular Thomas–Fermi differential equation for neutral atoms is solved using the fractional order of rational Chebyshev orthogonal functions (FRCs) of the first kind, FTnα(t,L), on a semi-infinite domain, where L is an arbitrary numerical parameter. First, using the quasilinearization method, the equation be converted into a sequence of linear ordinary differential equations (LDEs), and then these LDEs are solved using the FRCs collocation method. Using 300 collocation points, we have obtained a very good approximation solution and the value of the initial slope y′(0)=−1.5880710226113753127186845094239501095, highly accurate to 37 decimal places.