Approximate polynomial solutions of the nonlinear Lane–Emden type equations arising in astrophysics using the squared remainder minimization method

In this paper we use a recently introduced approximation method to compute analytical approximate polynomial solutions for some well-known classes of Lane–Emden type equations. The method, called the squared remainder minimization method, is tested on several applications of the Lane–Emden equations including the standard Lane–Emden equation, the white-dwarf equation and the isothermal gas spheres equation. The results of an extensive comparison with previous results emphasizes the accuracy of the method.