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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 195310, 11 pages
http://dx.doi.org/10.1155/2012/195310
Research Article

The Solution of a Class of Third-Order Boundary Value Problems by the Reproducing Kernel Method

1Department of Mathematics, Inner Mongolia University of Technology, Hohhot 010051, China
2Jining Teachers College, Jining 012000, China

Received 1 July 2012; Accepted 20 September 2012

Academic Editor: Wing-Sum Cheung

Copyright © 2012 Zhiyuan Li et al. 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

This paper expands the application of reproducing kernel method to a class of third-order boundary value problems with mixed nonlinear boundary conditions. The analytical solution is represented in the form of series in the reproducing kernel space. The -term approximation is obtained and is proved to converge to the analytical solution. The numerical examples are given to demonstrate the computation efficiency of the presented method. Results obtained by the method indicate that the method is simple and effective.