Elementary Analysis of Lane-Emden Equation by Successive Differentiation Method

Abstract

This universe has veiled many secrets for mankind. On exploring them mathematically several differential equations have been created. Lane-Emden Equation (LEE) is among the most famous equations concerned with the study of stellar structure. The main purpose of this work is to show the effectiveness of a numerical method named Successive Differentiation Method (SDM) which can obtain analytical solutions for nonlinear singular differential equations. To establish the claim, the nonlinear singular boundary and initial value problem of Lane-Emden that governs the polytropic and isothermal gas spheres is considered here. Different illustrative types of Lane-Emden Equation have been solved numerically in this paper and these numerical results are compared with the numerical results of formerly solved numerical techniques. SDM proved to be the easiest method not only in accuracy but also in tranquil implementation of numerical techniques over the entire finite domain.