Science and Education Publishing American Journal of Applied Mathematics and Statistics 2328-7292 1 1 2013 10 08 Wavelet-Galerkin Method and Some Numerical Method for Lane-Emden Type Differential Equation 83 86 EN Jafar Biazar Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Guilan, Rasht, Iran Fereshteh Goldoust AJAMS2013151 10.12691/ajams-1-5-1 2013 08 09 2013 09 21 2013 10 08 In this paper, we will compare the performance of Adomian decomposition method and the wavelet-Galerkin method applied to the Lane-Emden type differential equation. The Galerkin Wavelet method (GWM), which is known as a numerical approach is used for the Lane- Emden equation, as an initial value problem. This approach consists of using integral operator, to convert the Lane- Emden equation in to an integral equation, then applying Galerkin Wavelet method to solve the resulted integral equation. The properties of Galerkin Wavelet method (GWM) and the Adomian Decomposition Method are also addressed. Although the Adomian decomposition solution required slightly more computational effort than the wavelet-Galerkin solution, it resulted in more accurate results than the wavelet-Galerkin method. To illustrate the methods two examples are provided and the results are in good agreement with exact solution.