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Abstract and Applied Analysis
Volume 2014, Article ID 379829, 8 pages
http://dx.doi.org/10.1155/2014/379829
Research Article

Three-Step Block Method for Solving Nonlinear Boundary Value Problems

1Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia
2Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia

Received 13 December 2013; Revised 26 April 2014; Accepted 8 May 2014; Published 5 June 2014

Academic Editor: Abdon Atangana

Copyright © 2014 Phang Pei See et al. 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 propose a three-step block method of Adam’s type to solve nonlinear second-order two-point boundary value problems of Dirichlet type and Neumann type directly. We also extend this method to solve the system of second-order boundary value problems which have the same or different two boundary conditions. The method will be implemented in predictor corrector mode and obtain the approximate solutions at three points simultaneously using variable step size strategy. The proposed block method will be adapted with multiple shooting techniques via the three-step iterative method. The boundary value problem will be solved without reducing to first-order equations. The numerical results are presented to demonstrate the effectiveness of the proposed method.