A numerical approach for solving a class of the nonlinear Lane-Emden type equations arising in astrophysics

摘要

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.