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Rational Legendre pseudospectral approach for solving nonlinear differential equations of Lane-Emden type. (English) Zbl 1177.65100
Summary: The Lane-Emden equation is a nonlinear singular equation in astrophysics that corresponds to the polytropic models. In this paper, a pseudospectral technique is proposed to solve the Lane-Emden type equations on a semi-infinite domain. The method is based on rational Legendre functions and Gauss-Radau integration. The method reduces solving the nonlinear ordinary differential equation to solve a system of nonlinear algebraic equations. The comparison of the results with the other numerical methods shows the efficiency and accuracy of this method.

##### MSC:
 65L05 Numerical methods for initial value problems 65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems, general theory 85A15 Galactic and stellar structure
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