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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.
65L05Initial value problems for ODE (numerical methods)
65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE
34A34Nonlinear ODE and systems, general
85A15Galactic and stellar structure
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