Efficient boundary value problem solution for a Lane-Emden equation

Abstract

An efficient method for determining an initial guess to an iterative solution to the boundary value problem y′′ + (k=x)y′ + $delta e^ y$ey = 0 solved subject to y′(0) = 0 and y(1) = 0 is proposed. This initial guess overcomes the instability that occurs at the boundary y′(0) = 0 for k ≤ 1. When the iterative method becomes singular we can conclude that the maximum value of the critical parameter $delta e^ y$ has been determined.