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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:
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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