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Math. Comput. Appl. 2010, 15(4), 613-620; doi:10.3390/mca15040613

Efficient Boundary Value Problem Solution for a Lane-Emden Equation

Centre for Differential Equations, Continuum Mechanics and Applications School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits 2050, South Africa
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Published: 1 December 2010
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Abstract

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.
Keywords: Lane-Emden equation; boundary value problem; approximate solution Lane-Emden equation; boundary value problem; approximate solution
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Harley, C.; Momoniat, E. Efficient Boundary Value Problem Solution for a Lane-Emden Equation. Math. Comput. Appl. 2010, 15, 613-620.

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