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
Copyright Status
Unknown
Socpus ID
50349103358 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/50349103358
STARS Citation
Van Gorder, Robert A. and Vajravelu, K., "Analytic And Numerical Solutions To The Lane-Emden Equation" (2008). Scopus Export 2000s. 9802.
https://stars.library.ucf.edu/scopus2000/9802