## A Jacobi-Gauss collocation method for solving nonlinear Lane-Emden type equations.(English)Zbl 1244.65099

Summary: A shifted Jacobi-Gauss collocation spectral method is proposed for solving the nonlinear Lane-Emden type equation. The spatial approximation is based on shifted Jacobi polynomials $$P_{T,n}^{(\alpha ,\beta)}(x)$$ with $$\alpha , \beta \in ( - 1, \infty ), ~T > 0$$, and $$n$$ is the polynomial degree. The shifted Jacobi-Gauss points are used as collocation nodes. Numerical examples are included to demonstrate the validity and applicability of the technique and a comparison is made with existing results. The method is easy to implement and yields very accurate results.

### MSC:

 65L05 Numerical methods for initial value problems involving ordinary differential equations 65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems

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