Using reproducing kernel for solving a class of singular weakly nonlinear boundary value problems

Abstract

Cui et al. [M. Cui and F. Geng, Solving singular two point boundary value problems in reproducing kernel space, J. Comput. Appl. Math. 205 (2007), pp. 6–15; H. Yao and M. Cui, A new algorithm for a class of singular boundary value problems, Appl. Math. Comput. 186 (2007), pp. 1183–1191] presents an algorithm to solve a class of singular linear boundary value problems in the reproducing kernel space. In this paper, we will present three new algorithms to solve a class of singular weakly nonlinear boundary value problems in reproducing kernel space. The algorithms are efficiently applied to solving some model problems. It is demonstrated by the numerical examples that those algorithms are highly accurate.

Keywords:

• exact solution
• approximate solution
• singular boundary value problem
• weakly nonlinear problems
• reproducing kernel space

2000 AMS Subject Classification :

• 34B16
• 65L10

Acknowledgements

The author thanks the reviewers for their valuable suggestions, which greatly improved the paper. This paper is supported by the key project of Inner Mongolia University of Technology (No. ZD200709), the key project of Inner Mongolia (No. NJZY07066) and the NSF of China (No. 10461005).