A Jacobi-Gauss collocation method for solving nonlinear Lane-Emden type equations

被引:116
作者
Bhrawy, A. H. [1 ]
Alofi, A. S. [1 ]
机构
[1] King Abdulaziz Univ, Fac Sci, Dept Math, Jeddah, Saudi Arabia
关键词
Lane-Emden type equation; Second-order initial value problems; Collocation method; Jacobi-Gauss quadrature; Shifted Jacobi polynomials; SPECTRAL-GALERKIN ALGORITHMS; INITIAL-VALUE PROBLEMS; DIFFERENTIAL-EQUATIONS; SINGULAR IVPS; APPROXIMATE SOLUTION;
D O I
10.1016/j.cnsns.2011.04.025
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, 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,beta((x,beta)) (x) with alpha, beta is an element of (-1, infinity), 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. (C) 2011 Elsevier B.V. All rights reserved.
引用
收藏
页码:62 / 70
页数:9
相关论文
共 35 条
[1]   On using a modified Legendre-spectral method for solving singular IVPs of Lane-Emden type [J].
Adibi, H. ;
Rismani, A. M. .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2010, 60 (07) :2126-2130
[2]   Second order initial value problems of Lane-Emden type [J].
Agarwal, Ravi P. ;
O'Regan, Donal .
APPLIED MATHEMATICS LETTERS, 2007, 20 (12) :1198-1205
[3]  
[Anonymous], INTRO STUDY STELLAR
[4]  
[Anonymous], 2000, SIAM
[5]  
[Anonymous], 1998, A Practical Guide to Pseudospectral Methods
[6]  
[Anonymous], APPL MATH COMPUT
[7]  
[Anonymous], J EGYPT MATH SOC
[8]  
[Anonymous], COMPUT PHYS COMMUN
[9]   A generalization of the Lane-Emden equation [J].
Aslanov, Afgan .
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2008, 85 (11) :1709-1725
[10]   Homotopy analysis method for singular IVPs of Emden-Fowler type [J].
Bataineh, A. Sami ;
Noorani, M. S. M. ;
Hashim, I. .
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2009, 14 (04) :1121-1131