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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
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems, general theory
Software:
Matlab
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