Title

Analytic And Numerical Solutions To The Lane-Emden Equation

Keywords

Analytical solution; Gravitational potential; Lane-Emden equation; Nonlinear ordinary differential equation; Numerical solution

Abstract

In this Letter, we present analytical solutions to the Lane-Emden equation y″ (x) + frac(2, x) y′ (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. © 2008 Elsevier B.V. All rights reserved.

Publication Date

9-22-2008

Publication Title

Physics Letters, Section A: General, Atomic and Solid State Physics

Volume

372

Issue

39

Number of Pages

6060-6065

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.physleta.2008.08.002

Socpus ID

50349103358 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/50349103358

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