%0 Journal Article
%T A parametric iteration method for solving Lane-Emden type equations
%J Iranian Journal of Numerical Analysis and Optimization
%I Ferdowsi University of Mashhad
%Z 2423-6977
%A Chaharpashlou, R.
%D 2017
%\ 04/01/2017
%V 7
%N 1
%P 33-46
%! A parametric iteration method for solving Lane-Emden type equations
%K Piecewise-truncated parametric iteration method
%K Truncated parametric iteration method
%K Parametric iteration method
%K Nonlinear Lane- Emden type equations
%R 10.22067/ijnao.v7i1.39519
%X 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 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 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 eﬃciency and accuracy of the proposed method.
%U https://ijnao.um.ac.ir/article_24506_20eb4f21f86c9f6d57ef73d3c0a2f835.pdf