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Three-step block method for solving nonlinear boundary value problems

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 cond...

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Main Authors: Phang, Pei See, Abdul Majid, Zanariah, Suleiman, Mohamed
Format: Article
Language:English
Published: Hindawi Publishing Corporation 2014
Online Access:http://psasir.upm.edu.my/id/eprint/35851/1/Three-Step%20Block%20Method%20for%20Solving%20Nonlinear%20Boundary.pdf
http://psasir.upm.edu.my/id/eprint/35851/
http://www.hindawi.com/journals/aaa/2014/379829/abs/
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spelling my.upm.eprints.358512016-02-10T08:48:21Z http://psasir.upm.edu.my/id/eprint/35851/ Three-step block method for solving nonlinear boundary value problems Phang, Pei See Abdul Majid, Zanariah Suleiman, Mohamed 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. Hindawi Publishing Corporation 2014 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/35851/1/Three-Step%20Block%20Method%20for%20Solving%20Nonlinear%20Boundary.pdf 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 http://www.hindawi.com/journals/aaa/2014/379829/abs/ 10.1155/2014/379829
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
description 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.
format Article
author Phang, Pei See
Abdul Majid, Zanariah
Suleiman, Mohamed
spellingShingle Phang, Pei See
Abdul Majid, Zanariah
Suleiman, Mohamed
Three-step block method for solving nonlinear boundary value problems
author_facet Phang, Pei See
Abdul Majid, Zanariah
Suleiman, Mohamed
author_sort Phang, Pei See
title Three-step block method for solving nonlinear boundary value problems
title_short Three-step block method for solving nonlinear boundary value problems
title_full Three-step block method for solving nonlinear boundary value problems
title_fullStr Three-step block method for solving nonlinear boundary value problems
title_full_unstemmed Three-step block method for solving nonlinear boundary value problems
title_sort three-step block method for solving nonlinear boundary value problems
publisher Hindawi Publishing Corporation
publishDate 2014
url http://psasir.upm.edu.my/id/eprint/35851/1/Three-Step%20Block%20Method%20for%20Solving%20Nonlinear%20Boundary.pdf
http://psasir.upm.edu.my/id/eprint/35851/
http://www.hindawi.com/journals/aaa/2014/379829/abs/
_version_ 1643831576297996288
score 13.244368

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