Title

Analytic and numerical solutions to the Lane-Emden equation

Authors

Authors

R. A. Van Gorder;K. Vajravelu

Comments

Authors: contact us about adding a copy of your work at STARS@ucf.edu

Abbreviated Journal Title

Phys. Lett. A

Keywords

Lane-Emden equation; Gravitational potential; Nonlinear ordinary; differential equation; Analytical solution; Numerical Solution; HOMOTOPY ANALYSIS METHOD; Physics, Multidisciplinary

Abstract

In this Letter, we present analytical solutions to the Lane-Emden equation y ''(x) + 2/xy'(x) + f(y) = 0 describing the thermal behavior of a spherical cloud of gas acting under the mutual attraction of its molecules. Solutions are obtained by using the traditional power series approach and by using the Homotopy Analysis Method (HAM). We show that the series solutions obtained by the Homotopy Analysis Method converge in a larger interval than in the case of the corresponding traditional series solutions. Furthermore, we obtained numerical solutions (using Runge-Kutta-Fehlberg 4-5 technique) which are used to validate the analytical solutions. (c) 2008 Elsevier B.V. All rights reserved.

Journal Title

Physics Letters A

Volume

372

Issue/Number

39

Publication Date

1-1-2008

Document Type

Article

Language

English

First Page

6060

Last Page

6065

WOS Identifier

WOS:000260063700004

ISSN

0375-9601

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