Journal of Applied Mathematics
Volume 2012 (2012), Article ID 891519, 18 pages
http://dx.doi.org/10.1155/2012/891519
Research Article

Iterative Method for Solving the Second Boundary Value Problem for Biharmonic-Type Equation

Dang Quang A.1 and Nguyen Van Thien2

1Institute of Information Technology, VAST, 18 Hoang Quoc Viet, Cau Giay, Hanoi 10000, Vietnam
2Hanoi University of Industry, Minh Khai, Tu Liem, Hanoi 10000, Vietnam

Received 8 April 2012; Revised 11 June 2012; Accepted 11 June 2012

Academic Editor: Carla Roque

Copyright © 2012 Dang Quang A. and Nguyen Van Thien. 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

Solving boundary value problems (BVPs) for the fourth-order differential equations by the reduction of them to BVPs for the second-order equations with the aim to use the achievements for the latter ones attracts attention from many researchers. In this paper, using the technique developed by ourselves in recent works, we construct iterative method for the second BVP for biharmonic-type equation, which describes the deflection of a plate resting on a biparametric elastic foundation. The convergence rate of the method is established. The optimal value of the iterative parameter is found. Several numerical examples confirm the efficiency of the proposed method.