A variational iteration method for solving nonlinear Lane-Emden problems

- A semi-analytical method for nonlinear Lane-Emden problems.
- Includes adaptive step size and domain decomposition.
- Overcomes the main difficulty arising in the singularity of the equation at the origin point.
- Is simple to implement, accurate when applied to Lane-Emden type equations.

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.