The variational iteration method for solving the Volterra integro-differential forms of the Lane-Emden and the Emden-Fowler problems with initial and boundary value conditions

Abstract

In this paper, the variational iteration method (VIM) is used to examine the Volterra integro-differential forms of the singular Lane-Emden and the Emden-Fowler initial value problems and boundary value problems arising in physics, astrophysics and stellar structures. The Volterra integro-differential forms of the Lane-Emden and the Emden-Fowler equations overcome the singularity behavior at the origin x = 0. The Lagrange multiplier, needed for the VIM, is λ = -1 for the various cases of the specified equations having distinct shape factors. We illustrate our work by analyzing few initial value problems and boundary value problems to emphasize the convergence of the acquired results.