A variational iteration method for solving nonlinear Lane–Emden problems

Abstract

In this paper, an explicit analytical method called the variational iteration method is presented for solving the second-order singular initial value problems of the Lane–Emden type. In addition, the local convergence of the method is discussed. It is often useful to have an approximate analytical solution to describe the Lane–Emden type equations, especially in the case that the closed-form solutions do not exist at all. This convince us that an effective improvement of the method will be useful to obtain a better approximate analytical solution. The improved method is then treated as a local algorithm in a sequence of intervals. Besides, an adaptive version is suggested for finding accurate approximate solutions of the nonlinear Lane–Emden type equations. Some examples are given to demonstrate the efficiency and accuracy of the proposed method.