Abstract and Applied Analysis

Three-Step Block Method for Solving Nonlinear Boundary Value Problems

Phang Pei See, Zanariah Abdul Majid, and Mohamed Suleiman

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 379829, 8 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412279770

Digital Object Identifier
doi:10.1155/2014/379829

Mathematical Reviews number (MathSciNet)
MR3219366

Zentralblatt MATH identifier
07022265

Citation

See, Phang Pei; Abdul Majid, Zanariah; Suleiman, Mohamed. Three-Step Block Method for Solving Nonlinear Boundary Value Problems. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 379829, 8 pages. doi:10.1155/2014/379829. https://projecteuclid.org/euclid.aaa/1412279770


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