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Three-step block method for solving nonlinear boundary value problems


Phang, Pei See and Abdul Majid, Zanariah and Suleiman, Mohamed (2014) Three-step block method for solving nonlinear boundary value problems. Abstract and Applied Analysis, 2014. art. no. 379829. pp. 1-8. ISSN 1085-3375; ESSN: 1687-0409


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.

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Additional Metadata

Item Type: Article
Divisions: Faculty of Science
Institute for Mathematical Research
DOI Number: https://doi.org/10.1155/2014/379829
Publisher: Hindawi Publishing Corporation
Keywords: Three-step block method; Nonlinear boundary value problems; Dirichlet type; Neumann type
Depositing User: Nurul Ainie Mokhtar
Date Deposited: 10 Feb 2016 08:48
Last Modified: 10 Feb 2016 08:48
Altmetrics: http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.1155/2014/379829
URI: http://psasir.upm.edu.my/id/eprint/35851
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