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An approximation algorithm for the solution of the nonlinear Lane-Emden type equations arising in astrophysics using Hermite functions collocation method. (English) Zbl 1216.65098
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:
65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE
65L05Initial value problems for ODE (numerical methods)
34A34Nonlinear ODE and systems, general
85A15Galactic and stellar structure
85A30Hydrodynamic and hydromagnetic problems in astrophysics
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