a parametric iteration method for solving laneemden type equations

In this paper, an analytical method called the parametric iteration method (pim) is presented for solving the secondorder singular ivps of laneemden type, and its local convergence is discussed. since it is often useful to have an approximate analytical solution to describe the laneemden type equa tions, especially for ones where the closedform solutions do not exist at all, therefore, an effective improvement of the pim is further proposed that is ca pable of obtaining an approximate analytical solution. the improved pim is finally treated as an algorithm in a sequence of intervals for finding accurate approximate solutions of the nonlinear laneemden type equations. also, we show how to identify an approximate optimal value of the convergence accelerating parameter within the frame of the method. some examples are given to demonstrate the efficiency and accuracy of the proposed method.