Rational Legendre pseudospectral approach for solving nonlinear differential equations of Lane-Emden type

Authors:
K. Parand;M. Shahini;Mehdi Dehghan
Affiliations:
Department of Computer Science, Shahid Beheshti University, G. C., Tehran, Iran;Department of Computer Science, Shahid Beheshti University, G. C., Tehran, Iran;Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology, No. 424 Hafez Ave, Tehran, Iran
Venue:
Journal of Computational Physics
Year:
2009

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Abstract

Lane-Emden equation is a nonlinear singular equation in the 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.