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Direct integration of the third-order two point and multipoint Robin type boundary value problems

This numerical study exclusively focused on the direct two point diagonally multistep block method of order four (2DDM4) in the form of Adams-type formulas. The proposed predictor–corrector scheme was applied in this study to compute two equally spaced numerical solutions for the third-order two poi...

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Main Authors: Nadirah, Mohd Nasir, Zanariah, Abdul Majid, Fudziah, Ismail, Norfifah, Bachok
Format: Article
Language:English
Published: Elsevier 2021
Subjects:
QA Mathematics
Online Access:http://umpir.ump.edu.my/id/eprint/32338/1/Direct%20integration%20of%20the%20third-order%20two%20point%20and%20multipoint%20Robin%20type%20boundary%20value%20problems.pdf
http://umpir.ump.edu.my/id/eprint/32338/
https://doi.org/10.1016/j.matcom.2020.10.028
https://doi.org/10.1016/j.matcom.2020.10.028
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spelling my.ump.umpir.323382021-11-05T04:10:02Z http://umpir.ump.edu.my/id/eprint/32338/ Direct integration of the third-order two point and multipoint Robin type boundary value problems Nadirah, Mohd Nasir Zanariah, Abdul Majid Fudziah, Ismail Norfifah, Bachok QA Mathematics This numerical study exclusively focused on the direct two point diagonally multistep block method of order four (2DDM4) in the form of Adams-type formulas. The proposed predictor–corrector scheme was applied in this study to compute two equally spaced numerical solutions for the third-order two point and multipoint boundary value problems (BVPs) subject to Robin boundary conditions concurrently at each step. The optimization of the computational costs was taken into consideration by not resolving the equation into a set of first-order differential equations. Instead, its implementation involved the use of shooting technique, which included the Newton divided difference formula employed for the iterative part, for the estimation of the initial guess. Apart from studying the local truncation error, the study also included the method analysis, including the order, stability, and convergence. The results of eight numerical problems demonstrated and highlighted competitive computational cost attained by the scheme, as compared to the existing method. Elsevier 2021-04 Article PeerReviewed pdf en http://umpir.ump.edu.my/id/eprint/32338/1/Direct%20integration%20of%20the%20third-order%20two%20point%20and%20multipoint%20Robin%20type%20boundary%20value%20problems.pdf Nadirah, Mohd Nasir and Zanariah, Abdul Majid and Fudziah, Ismail and Norfifah, Bachok (2021) Direct integration of the third-order two point and multipoint Robin type boundary value problems. Mathematics and Computers in Simulation, 182. pp. 411-427. ISSN 0378-4754 https://doi.org/10.1016/j.matcom.2020.10.028 https://doi.org/10.1016/j.matcom.2020.10.028
institution Universiti Malaysia Pahang
building UMP Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaysia Pahang
content_source UMP Institutional Repository
url_provider http://umpir.ump.edu.my/
language English
topic QA Mathematics
spellingShingle QA Mathematics
Nadirah, Mohd Nasir
Zanariah, Abdul Majid
Fudziah, Ismail
Norfifah, Bachok
Direct integration of the third-order two point and multipoint Robin type boundary value problems
description This numerical study exclusively focused on the direct two point diagonally multistep block method of order four (2DDM4) in the form of Adams-type formulas. The proposed predictor–corrector scheme was applied in this study to compute two equally spaced numerical solutions for the third-order two point and multipoint boundary value problems (BVPs) subject to Robin boundary conditions concurrently at each step. The optimization of the computational costs was taken into consideration by not resolving the equation into a set of first-order differential equations. Instead, its implementation involved the use of shooting technique, which included the Newton divided difference formula employed for the iterative part, for the estimation of the initial guess. Apart from studying the local truncation error, the study also included the method analysis, including the order, stability, and convergence. The results of eight numerical problems demonstrated and highlighted competitive computational cost attained by the scheme, as compared to the existing method.
format Article
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
title Direct integration of the third-order two point and multipoint Robin type boundary value problems
title_short Direct integration of the third-order two point and multipoint Robin type boundary value problems
title_full Direct integration of the third-order two point and multipoint Robin type boundary value problems
title_fullStr Direct integration of the third-order two point and multipoint Robin type boundary value problems
title_full_unstemmed Direct integration of the third-order two point and multipoint Robin type boundary value problems
title_sort direct integration of the third-order two point and multipoint robin type boundary value problems
publisher Elsevier
publishDate 2021
url http://umpir.ump.edu.my/id/eprint/32338/1/Direct%20integration%20of%20the%20third-order%20two%20point%20and%20multipoint%20Robin%20type%20boundary%20value%20problems.pdf
http://umpir.ump.edu.my/id/eprint/32338/
https://doi.org/10.1016/j.matcom.2020.10.028
https://doi.org/10.1016/j.matcom.2020.10.028
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score 13.211869

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