New algorithm based on Hermite wavelets and Green’s function to solve Thomas-Fermi type differential equations

Abstract

This article introduces a novel method using Hermite wavelets and Green’s function to solve Thomas-Fermi-type equations with specific boundary conditions. The equation is first transformed into an integral form and then expanded using Hermite wavelets to create an algebraic expression. The collocation technique generates a set of nonlinear equations, solved iteratively by methods like Newton-Raphson. Several examples demonstrate the method’s effectiveness and accuracy. It is useful for a range of linear and nonlinear differential equations in various fields. Comparative analysis shows it is more accurate and computationally efficient than traditional methods. All computations are performed using MAT LAB.