ACCURATE SOLUTIONS TO THE THOMAS-FERMI EQUATIONUSING THE HANKEL-PADÉ METHOD

JAVIER GARCIA; FRANCISCO M FERNÁNDEZ

Congreso; VIII Congreso de Matemática Aplicada, Computacional e Industrial; 2021

We consider the Thomas-Fermi equation both for isolated atoms and for atoms in strong magnetic fields.We employ the Hankel-Padé method to obtain the slope at origin of the solutions of these equations, significantly improving upon the results obtained before using the same method. We study the convergence rate of the method for both equations and, for the strong-magnetic-field equation, we obtain results accurate to more than 500 digits.