## Abstract and Applied Analysis

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

### Three-Step Block Method for Solving Nonlinear Boundary Value Problems

Phang Pei See, Zanariah Abdul Majid, and Mohamed Suleiman

#### 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