Solving of nonlinear differential equations with Homotopy and Adomian methods; Polytropic gas spheres case study

Abstract

In this paper, we will compare the Homotopy perturbation and the Adomian
decomposition methods for the exact solution with the aid of Mathematica package.
An approximate power series solution of the Lane-Emden second order differential
equation is represented here in analytical form by Homotopy perturbation method for any
value of the polytropic index (n).
The physical parameters of the stellar interior model with polytropic condition
(i. e. dQ?dT = constant); like mass, pressure, and temperature have been created with
analytical expressions with (n). Finally, we have study the Solar polytropic model with
(n = 3) due to our approximate analytical series solution and other analytical forms.