Laguerre wavelet method for solving Thomas–Fermi type equations

Abstract

An efficient numerical algorithm based on the Laguerre wavelets collocation technique for numerical solutions of a class of Thomas–Fermi boundary value problems, which arises in the study the charge densities and potential in many scientific models like in atoms, molecules, metals and crystals is presented. This technique includes the theory of Laguerre wavelets and the collocation technique. To avoid singular behavior at $$x=0$$ , we consider the equivalent integral form of the generalized Thomas–Fermi equation. We apply the Laguerre wavelets collocation technique to get a nonlinear system of equations having unknown Laguerre wavelet coefficients. The Newton–Raphson method is applied to analyze this nonlinear system of equations. We provide the error analysis of the present method. Several numerical problems are provided to test the effectiveness of the proposed method. The obtained results are compared by the exact solution and the results obtained by the other known techniques. The numerical results reveal that the current analysis provides a better approximation than existing methods.