A numerical approach for solving a class of the nonlinear Lane-Emden type equations arising in astrophysics
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.34, no.18, pp.2218-2230, 2011 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 34 Issue: 18
- Publication Date: 2011
- Doi Number: 10.1002/mma.1519
- Journal Name: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.2218-2230
- Keywords: nonlinear Lane-Emden type equations, collocation method, collocation points, Bessel polynomials and series, isothermal gas spheres, astrophysics, INITIAL-VALUE PROBLEMS, DIFFERENTIAL-EQUATIONS, SINGULAR IVPS, POLYNOMIAL SOLUTIONS, FOWLER EQUATIONS, ALGORITHM
- Akdeniz University Affiliated: No
Abstract
In this paper, a collocation method based on the Bessel polynomials is presented for the approximate solution of a class of the nonlinear Lane-Emden type equations, which have many applications in mathematical physics. The exact solution can be obtained if the exact solution is polynomial. In other cases, such as an increasing number of nodes, a good approximation can be obtained with applicable errors. In addition, the method is presented with error and stability analysis. The numerical results show the effectiveness of the method for this type of equations. Comparing the methodology with some known techniques shows that the present approach is relatively easy and highly accurate. Copyright (C) 2011 John Wiley & Sons, Ltd.