Abstract and Applied Analysis
Volume 2012 (2012), Article ID 414612, 9 pages
http://dx.doi.org/10.1155/2012/414612
Research Article

Approximate Solutions to Three-Point Boundary Value Problems with Two-Space Integral Condition for Parabolic Equations

Jing Niu,1,2 Yingzhen Lin,1 and Minggen Cui1

1Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
2School of Mathematics and Sciences, Harbin Normal University, Harbin 150025, China

Received 24 January 2012; Accepted 16 February 2012

Academic Editor: Chaitan Gupta

Copyright © 2012 Jing Niu 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

We construct a novel reproducing kernel space and give the expression of reproducing kernel skillfully. Based on the orthogonal basis of the reproducing kernel space, an efficient algorithm is provided firstly to solve a three-point boundary value problem of parabolic equations with two-space integral condition. The exact solution of this problem can be expressed by the series form. The numerical method is supported by strong theories. The numerical experiment shows that the algorithm is simple and easy to implement by the common computer and software.