Elementary Analysis of Lane-Emden Equation by Successive Differentiation Method

This universe has veiled many secrets for mankind. On exploringthem mathematically several differential equations have been created.Lane-Emden Equation (LEE) is among the most famous equations concernedwith the study of stellar structure. The main purpose of this workis to show the effectiveness of a numerical method named Successive DifferentiationMethod (SDM) which can obtain analytical solutions for nonlinearsingular differential equations. To establish the claim, the nonlinearsingular boundary and initial value problem of Lane-Emden that governsthe polytropic and isothermal gas spheres is considered here. Differentillustrative types of Lane-Emden Equation have been solved numericallyin this paper and these numerical results are compared with the numericalresults of formerly solved numerical techniques. SDM proved to be theeasiest method not only in accuracy but also in tranquil implementation ofnumerical techniques over the entire finite domain