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International Journal of Differential Equations
Volume 2013 (2013), Article ID 728149, 6 pages
http://dx.doi.org/10.1155/2013/728149
Research Article

Picard Type Iterative Scheme with Initial Iterates in Reverse Order for a Class of Nonlinear Three Point BVPs

Department of Mathematics, BITS Pilani, Pilani, Rajasthan 333031, India

Received 30 April 2013; Accepted 23 June 2013

Academic Editor: Yuji Liu

Copyright © 2013 Mandeep Singh and Amit K. Verma. 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 consider the following class of three point boundary value problem , , where , , the source term is Lipschitz and continuous. We use monotone iterative technique in the presence of upper and lower solutions for both well-order and reverse order cases. Under some sufficient conditions, we prove some new existence results. We use examples and figures to demonstrate that monotone iterative method can efficiently be used for computation of solutions of nonlinear BVPs.