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Advances in Numerical Analysis
Volume 2013 (2013), Article ID 470258, 5 pages
http://dx.doi.org/10.1155/2013/470258
Research Article

Iterative Method for Solving a Beam Equation with Nonlinear Boundary Conditions

1Institute of Information Technology, VAST, 18 Hoang Quoc Viet, Cau Giay, Hanoi 10000, Vietnam
2College of Science, Thai Nguyen University, Thai Nguyen City 23000, Vietnam

Received 3 June 2013; Accepted 16 July 2013

Academic Editor: Michele Benzi

Copyright © 2013 Quang A. Dang and Nguyen Thanh Huong. 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

In this paper, we propose an iterative method for solving a beam problem which is described by a nonlinear fourth-order equation with nonlinear boundary conditions. The method reduces this nonlinear fourth-order problem to a sequence of linear second-order problems with linear boundary conditions. The convergence of the method is proved, and some numerical examples demonstrate the efficiency of the method.