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A numerical approach for solving a class of the nonlinear Lane–Emden type equations arising in astrophysics
Author(s) -
Yüzbaşı Şuayip
Publication year - 2011
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1519
Subject(s) - mathematics , type (biology) , nonlinear system , bessel function , class (philosophy) , collocation method , polynomial , collocation (remote sensing) , exact solutions in general relativity , stability (learning theory) , numerical analysis , mathematical analysis , differential equation , computer science , physics , ecology , ordinary differential equation , quantum mechanics , artificial intelligence , machine learning , biology
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 © 2011 John Wiley & Sons, Ltd.