Approximate solution of a differential equation arising in astrophysics using the variational iteration method

The Lane–Emden equation is Poisson’s equation for the gravitational potential of a self-gravitating, spherically symmetric polytropic fluid which arises in many applications of mathematical physics and constitutes a good model for many systems in various fields. In this work, this equation is investigated using the variational iteration method. Application of variational iteration technique to this problem shows the efficiency and applicability of this procedure for solving this equation. This technique does not require any discretization, linearization or small perturbations and therefore reduces the numerical computations a lot.