Boundary Value Problems
Volume 2011 (2011), Article ID 929061, 17 pages
doi:10.1155/2011/929061
Research Article

Approximation of Solutions for Second-Order m-Point Nonlocal Boundary Value Problems via the Method of Generalized Quasilinearization

Ahmed Alsaedi

Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Received 11 May 2010; Revised 29 July 2010; Accepted 2 October 2010

Academic Editor: Gennaro Infante

Copyright © 2011 Ahmed Alsaedi. 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 discuss the existence and uniqueness of the solutions of a second-order m-point nonlocal boundary value problem by applying a generalized quasilinearization technique. A monotone sequence of solutions converging uniformly and quadratically to a unique solution of the problem is presented.