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.

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