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Zbl 1216.65098
Parand, K.; Dehghan, Mehdi; Rezaei, A.R.; Ghaderi, S.M.
An approximation algorithm for the solution of the nonlinear Lane-Emden type equations arising in astrophysics using Hermite functions collocation method. (English)
[J] Comput. Phys. Commun. 181, No. 6, 1096-1108 (2010). ISSN 0010-4655

Summary: We propose a collocation method for solving some well-known classes of Lane-Emden type equations which are nonlinear ordinary differential equations on the semi-infinite domain. They are categorized as singular initial value problems. The proposed approach is based on a Hermite function collocation method. To illustrate the reliability of the method, some special cases of the equations are solved as test examples. The new method reduces the solution of a problem to the solution of a system of algebraic equations. Hermite functions have prefect properties that make them useful to achieve this goal. We compare the present work with some well-known results and show that the new method is efficient and applicable.

MSC 2000:: *65L60 Finite numerical methods for ODE
65L05 Initial value problems for ODE (numerical methods)
34A34 Nonlinear ODE and systems, general
85A15 Galactic and stellar structure
85A30 Hydrodynamic and hydromagnetic problems in astrophysics

Keywords: Lane-Emden type equations; nonlinear ODE; collocation method; Hermite functions; isothermal gas spheres; astrophysics; numerical examples; singular initial value problems

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