Analytical Approach to Study the Generalized Lane-Emden Model Arises in the Study of Stellar Configuration

Authors

Fazal Abbas, Department of Mathermatics and Computer Sciences, Stetson University, USAFollow
Petko Kitanov, Deparment of Mathematical and Natural Sciences, Wells College, USAFollow
Sierra Chimene, Biomedical Engineering, Rochester Institute of Technology, USAFollow
Abbas Rehmani, Mechanical Engineering, Georgia Institute of Technology, USAFollow

Author Country (or Countries)

USA

Abstract

In this paper, we consider the generalized Lane-Emden model which arises in the study of steller configuration. We came up with the nonlinear, multi-singular, initial value ordinary differential equations. Mathematical induction is used to verify the generalized non-iterative higher-order Lane-Emden type equation. We use various Homotopy Analysis Method (HAM) algorithms to find the convergent series solutions of the model. It is observed how the choice of initial value, increasing values of M in the polynomial nonlinearity yM, and different choices of HAM algorithms impact the solution radius of convergence. Convergent series solutions obtained from HAM algorithms are compared with the traditional power series and Runge-Kutta-Fehlberg method (RKF45). The traditional series solution follows the actual solution in the domain where the actual solution is positive while HAM does not require domain restriction.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/140301

Recommended Citation

Abbas, Fazal; Kitanov, Petko; Chimene, Sierra; and Rehmani, Abbas (2020) "Analytical Approach to Study the Generalized Lane-Emden Model Arises in the Study of Stellar Configuration," Applied Mathematics & Information Sciences: Vol. 14: Iss. 3, Article 1.
DOI: http://dx.doi.org/10.18576/amis/140301
Available at: https://digitalcommons.aaru.edu.jo/amis/vol14/iss3/1