Boundary Value Problems
Volume 2010 (2010), Article ID 459754, 19 pages
doi:10.1155/2010/459754
Research Article

Existence and Numerical Method for Nonlinear Third-Order Boundary Value Problem in the Reproducing Kernel Space

Xueqin Lü1,2 and Minggen Cui1

1Department of Mathematics, Harbin Institute of Technology, Weihai, Shandong 264209, China
2School of Mathematics and Sciences, Harbin Normal University, Harbin, Heilongjiang 150025, China

Received 14 July 2009; Revised 12 November 2009; Accepted 11 January 2010

Academic Editor: Irena Rachůnkova

Copyright © 2010 Xueqin Lü and Minggen Cui. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We are concerned with general third-order nonlinear boundary value problems. An existence theorem of solution is given under weaker conditions. In the meantime, an iterative algorithm with global convergence is presented. The higher order derivatives of approximate solution is obtained by using this method can approximate the corresponding derivatives of exact solution well.