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An efficient method for determining an initial guess to an iterative solution to the boundary value problem y" + (k/x)y′ + δey = 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 β has been determined.

Efficient Boundary Value Problem Solution for a Lane-Emden Equation