A new algorithm for solving singular IVPs of Lane-Emden type. (English) Zbl 1343.65087
Mastorakis, N. (ed.) et al., Latest trends on applied mathematics, simulation, modelling. 4th international conference on applied mathematics, simulation, modelling (ASM’10), Corfu Island, Greece, July 22–25, 2010. Athens: WSEAS Press (ISBN 978-960-474-210-3; 978-960-474-212-7/cd-rom). Mathematics and Computers in Science and Engineering, 176-180 (2010).
Summary: The Lane-Emden equation that describes the temperature in a self-gravitating star has been widely studied due to its applications in astrophysics and as a prototype for testing new mathematical and numerical techniques for solving nonlinear equations. In this paper a new semi-analytical algorithm for solving singular initial value problems of Lane-Emden type is presented. Solutions for polytropic indices \(n=2\), 3 and 4 are found and compared with numerical results and the Sinc-collocation approximations in the literature. Our investigations indicate that there is excellent agreement between the numerical results and the new method. Excellent agreement is also found when comparing the results of the new method against the exact analytic solution of the Lane-Emden equation for polytropic index \(m=5\) showing the accuracy and computational efficiency of the present technique.
For the entire collection see [Zbl 1205.00093].
For the entire collection see [Zbl 1205.00093].
MSC:
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 65L60 | Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations |
| 85-08 | Computational methods for problems pertaining to astronomy and astrophysics |
| 85A04 | General questions in astronomy and astrophysics |
