Diagonal block method for solving two-point boundary value problems with Robin boundary conditions

This numerical study presents the diagonal block method of order four for solving the second-order boundary value problems (BVPs)with Robin boundary conditions at two-point concurrently using constant step size. The solution is obtained directly without reducing to a system of first-order differenti...

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Main Authors: Nadirah, Mohd Nasir, Zanariah, Abdul Majid, Fudziah, Ismail, Norfifah, Bachok
Format: Article
Language:English
Published: Hindawi Publishing Corporation 2018
Subjects:
Online Access:http://umpir.ump.edu.my/id/eprint/32346/1/PAPER%205.pdf
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author Nadirah, Mohd Nasir
Zanariah, Abdul Majid
Fudziah, Ismail
Norfifah, Bachok
author_facet Nadirah, Mohd Nasir
Zanariah, Abdul Majid
Fudziah, Ismail
Norfifah, Bachok
author_sort Nadirah, Mohd Nasir
collection UMP
description This numerical study presents the diagonal block method of order four for solving the second-order boundary value problems (BVPs)with Robin boundary conditions at two-point concurrently using constant step size. The solution is obtained directly without reducing to a system of first-order differential equations using a combination of predictor-corrector mode via shooting technique. The shooting method was adapted with the Newton divided difference interpolation approach as the strategy of seeking for the new initial estimate. Five numerical examples are included to examine and illustrate the practical usefulness of the proposed method. Numerical tested problem is also highlighted on the diffusion of heat generated application that imposed the Robin boundary conditions. The present findings revealed that the proposed method gives an efficient performance in terms of accuracy, total function calls, and execution time as compared with the existing method.
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spelling UMPir323462021-11-08T07:33:25Z http://umpir.ump.edu.my/id/eprint/32346/ Diagonal block method for solving two-point boundary value problems with Robin boundary conditions Nadirah, Mohd Nasir Zanariah, Abdul Majid Fudziah, Ismail Norfifah, Bachok QA Mathematics This numerical study presents the diagonal block method of order four for solving the second-order boundary value problems (BVPs)with Robin boundary conditions at two-point concurrently using constant step size. The solution is obtained directly without reducing to a system of first-order differential equations using a combination of predictor-corrector mode via shooting technique. The shooting method was adapted with the Newton divided difference interpolation approach as the strategy of seeking for the new initial estimate. Five numerical examples are included to examine and illustrate the practical usefulness of the proposed method. Numerical tested problem is also highlighted on the diffusion of heat generated application that imposed the Robin boundary conditions. The present findings revealed that the proposed method gives an efficient performance in terms of accuracy, total function calls, and execution time as compared with the existing method. Hindawi Publishing Corporation 2018-10-02 Article PeerReviewed pdf en http://umpir.ump.edu.my/id/eprint/32346/1/PAPER%205.pdf Nadirah, Mohd Nasir and Zanariah, Abdul Majid and Fudziah, Ismail and Norfifah, Bachok (2018) Diagonal block method for solving two-point boundary value problems with Robin boundary conditions. Mathematical Problems in Engineering, 2018. pp. 1-12. ISSN 1024-123X (print); 1563-5147 (online). (Published) https://doi.org/10.1155/2018/2056834 https://doi.org/10.1155/2018/2056834
spellingShingle QA Mathematics
Nadirah, Mohd Nasir
Zanariah, Abdul Majid
Fudziah, Ismail
Norfifah, Bachok
Diagonal block method for solving two-point boundary value problems with Robin boundary conditions
title Diagonal block method for solving two-point boundary value problems with Robin boundary conditions
title_full Diagonal block method for solving two-point boundary value problems with Robin boundary conditions
title_fullStr Diagonal block method for solving two-point boundary value problems with Robin boundary conditions
title_full_unstemmed Diagonal block method for solving two-point boundary value problems with Robin boundary conditions
title_short Diagonal block method for solving two-point boundary value problems with Robin boundary conditions
title_sort diagonal block method for solving two point boundary value problems with robin boundary conditions
topic QA Mathematics
url http://umpir.ump.edu.my/id/eprint/32346/1/PAPER%205.pdf
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AT norfifahbachok diagonalblockmethodforsolvingtwopointboundaryvalueproblemswithrobinboundaryconditions