Using Hermite Function for Solving Thomas-Fermi Equation

TL;DR

This paper introduces a Hermite collocation method for solving the nonlinear Thomas-Fermi equation on a semi-infinite interval, demonstrating improved accuracy and convergence over existing methods.

Contribution

The paper presents a novel Hermite collocation approach specifically designed for the Thomas-Fermi equation, enhancing solution accuracy and computational efficiency.

Findings

More accurate solutions than existing methods

Faster convergence demonstrated

Effective for nonlinear differential equations on semi-infinite intervals

Abstract

In this paper, we propose Hermite collocation method for solving Thomas-Fermi equation that is nonlinear ordinary differential equation on semi-infinite interval. This method reduces the solution of this problem to the solution of a system of algebraic equations. We also present the comparison of this work with solution of other methods that shows the present solution is more accurate and faster convergence in this problem.