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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.

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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