A Nonclassical Radau Collocation Method for Nonlinear Initial-Value Problems with Applications to Lane-Emden Type Equations

We propose a numerical method for solving nonlinear initial-value problems of Lane-Emden type. The method is based upon nonclassical Gauss-Radau collocation points, and weighted interpolation. Nonclassical orthogonal polynomials, nonclassical Radau points and weighted interpolation are introduced on...

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Bibliographic Details
Published in:Journal of Applied Mathematics 2012-01, Vol.2012 (2012), p.66-78-006
Main Authors: Maleki, Mohammad, Tavassoli Kajani, M., Hashim, I., Kilicman, A., Atan, K. A. M.
Format: Article
Language:English
Subjects:
Accuracy
Astrophysics
Methods
Ordinary differential equations
Polynomials
Studies
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Summary:We propose a numerical method for solving nonlinear initial-value problems of Lane-Emden type. The method is based upon nonclassical Gauss-Radau collocation points, and weighted interpolation. Nonclassical orthogonal polynomials, nonclassical Radau points and weighted interpolation are introduced on arbitrary intervals. Then they are utilized to reduce the computation of nonlinear initial-value problems to a system of nonlinear algebraic equations. We also present the comparison of this work with some well-known results and show that the present solution is very accurate.
ISSN:1110-757X
1687-0042
DOI:10.1155/2012/103205