Efficient boundary value problem solution for a Lane-Emden equation (Q636100)

Summary: An efficient method for determining an initial guess to an iterative solution to the boundary value problem \(y''+(k/x)y'+\delta e^y=0\) 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 \(k\leq 1\). When the iterative method becomes singular we can conclude that the maximum value of the critical parameter \(\delta\) has been determined.