Approximate Solutions to Lane-Emden Equation for Stellar Configuration

Authors

Fazal Abbas, Department of Mathematics and Computer Sciences, Stetson University, Florida, USAFollow
Petko Kitanov, School of Mathematical Sciences, Rochester Institute of Technology, New York, USAFollow
Shoshanna Longo, Computer Engineering, Rochester Institute of Technology, New York, USAFollow

Author Country (or Countries)

USA

Abstract

In this paper, we consider the Lane-Emden equation of the first kind which arises in the study of stellar structures. We use multiple algorithms, based on Homotopy Analysis Method (HAM) to find the convergent series solutions to the singular, non-linear, initial value problem. It is found that the radius of convergence for the solutions is affected by three factors: the choice of initial value, the order and type of non-linearity, and the linear operator used. We then compare analytical results to the 20th order series solution, the Pade approximant to the series, and the approximate solution obtained via the Runge-Kutta-Fehlberg method (RKF45).

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/130201

Recommended Citation

Abbas, Fazal; Kitanov, Petko; and Longo, Shoshanna (2019) "Approximate Solutions to Lane-Emden Equation for Stellar Configuration," Applied Mathematics & Information Sciences: Vol. 13: Iss. 2, Article 1.
DOI: http://dx.doi.org/10.18576/amis/130201
Available at: https://digitalcommons.aaru.edu.jo/amis/vol13/iss2/1