Dynamically Consistent Approximate Rational Solutions to the Thomas-Fermi Equation
Classical Analysis and ODEs
2020-11-20 v1 Mathematical Physics
math.MP
Abstract
We construct two rational approximate solutions to the Thomas-Fermi (TF) nonlinear differential equation. These expressions follow from an application of the principle of dynamic consistency. In addition to examining differences in the predicted numerical values of the two approximate solutions, we compare these values with an accurate numerical solution obtained using a fourth-order Runge-Kutta method. We also present several new integral relations satisfied by the bounded solutions of the TF equation
Cite
@article{arxiv.2011.09889,
title = {Dynamically Consistent Approximate Rational Solutions to the Thomas-Fermi Equation},
author = {Ronald E. Mickens and Isom H. Herron},
journal= {arXiv preprint arXiv:2011.09889},
year = {2020}
}
Comments
10 pages, 2 figures