International Journal of Differential Equations
Volume 2011 (2011), Article ID 679528, 31 pages
http://dx.doi.org/10.1155/2011/679528
Research Article

A High Order Iterative Scheme for a Nonlinear Kirchhoff Wave Equation in the Unit Membrane

Le Thi Phuong Ngoc1 and Nguyen Thanh Long2

1Nhatrang Educational College, 01 Nguyen Chanh Street, Nhatrang City, Vietnam
2Department of Mathematics and Computer Science, University of Natural Science, Vietnam National University Ho Chi Minh City, 227 Nguyen Van Cu Street, District 5, Ho Chi Minh City, Vietnam

Received 5 May 2011; Accepted 16 October 2011

Academic Editor: Bashir Ahmad

Copyright © 2011 Le Thi Phuong Ngoc and Nguyen Thanh Long. 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

A high-order iterative scheme is established in order to get a convergent sequence at a rate of order 𝑁 ( 𝑁 ≥ 1 ) to a local unique weak solution of a nonlinear Kirchhoff wave equation in the unit membrane. This extends a recent result in (EJDE, 2005, No. 138) where a recurrent sequence converges at a rate of order 2.