An efficient pseudospectral method for numerical solution of nonlinear singular initial and boundary value problems arising in astrophysics

Abstract

In the manuscript, a pseudospectral method is developed for approximate and efficient solution of nonlinear singular Lane–Emden–Fowler initial and boundary value problems arising in astrophysics. In the proposed method, the Gauss pseudospectral method is utilized to reduce the problem to the solution of a system of algebraic equations. Furthermore, the Gauss pseudospectral method is developed for finding the first zero of the solution of this equation that gives the radius of the star, in which the numerous properties of the star such as mass, central pressure, and binding energy can be computed through their relations to this solution. The main advantage of the proposed method is that good results are obtained even by using a small number of discretization points and the rate of convergence is high. The accuracy and performance of the proposed method are examined by means of some numerical experiments. Copyright © 2015 John Wiley & Sons, Ltd.