Boundary Value Problems
Volume 2009 (2009), Article ID 320606, 17 pages
doi:10.1155/2009/320606
Research Article

Robust Monotone Iterates for Nonlinear Singularly Perturbed Boundary Value Problems

Igor Boglaev

Institute of Fundamental Sciences, Massey University, Private Bag 11-222, 4442 Palmerston North, New Zealand

Received 8 April 2009; Accepted 11 May 2009

Academic Editor: Donal O'Regan

Copyright © 2009 Igor Boglaev. 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 is concerned with solving nonlinear singularly perturbed boundary value problems. Robust monotone iterates for solving nonlinear difference scheme are constructed. Uniform convergence of the monotone methods is investigated, and convergence rates are estimated. Numerical experiments complement the theoretical results.