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Analytical solutions to a quasilinear differential equation related to the Lane–Emden equation of the second kind

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Abstract

We apply the δ-expansion method to a transformed Lane–Emden equation. The results are then transformed back, and we recover analytical solutions to the Lane–Emden equation of the second kind (which describes Bonnor–Ebert gas spheres) in a special case. The rapid convergence of the method results in qualitatively accurate solutions in relatively few iterations, as we see when we compare the obtained analytical solutions to numerical results.

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  1. Department of Mathematics, University of Central Florida, P.O. Box 161364, Orlando, FL 32816-1364, USA

    Robert A. Van Gorder

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  1. Robert A. Van Gorder
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Correspondence to Robert A. Van Gorder.

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Van Gorder, R.A. Analytical solutions to a quasilinear differential equation related to the Lane–Emden equation of the second kind. Celest Mech Dyn Astr 109, 137–145 (2011). https://doi.org/10.1007/s10569-010-9318-y

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