Spectral collocation methods for a class of nonlinear singular boundary value problems

In this paper, we deals with the numerical solutions of a class of nonlinear singular boundary value problems defined on bounded interval by regularization method and spectral-collocation method that approximate the exact solution of the singular boundary value problems. Legendre-Gauss-Lobatto nodes are used to collocate nodes. Efficient algorithms is implemented. Numerical results demonstrate its efficiency and high accuracy of this approach. The proposed method can be applicable to the cases that the singularity order of regular singular point is an arbitrary positive number.