Monotonous enclosures for the Thomas-Fermi equation in the isolated neutral atom case

Please address any correspondence to: C. Grossmann, Department of Mathematics, Kuwait University, PO Box 5969, Safat 13060, Kuwait A numerical method for the generation of enclosures for thesolution of the Thomas–Fermi equation on a semi-infiniteinterval is proposed. The method is based on the monotone discretizationprinciple and on available global bounds for the solution. Theconvergence of the new method on refined and extended gridsis investigated where available bounds are used to increasethe local step size with increasing arguments.