A parametric iteration method forsolving Lane-Emden type equations

In this paper, an analytical method called the parametric iteration method (PIM) is presented for solving the second-order singular IVPs of Lane-Emden type, and its local convergence is discussed. Since it is often useful to have an approximate analytical solution to describe the Lane-Emden type equa- tions, especially for ones where the closed-form solutions do not exist at all,therefore, an e ective improvement of the PIM is further proposed that is ca- pable of obtaining an approximate analytical solution. The improved PIM is nally treated as an algorithm in a sequence of intervals for nding accurateapproximate solutions of the nonlinear Lane-Emden 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 e ciency and accuracy of the proposed method.

Keywords:

Piecewise-truncated parametric iteration method , Truncated parametric iteration method , Parametric iteration method , Nonlinear Lane-Emden type equations