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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| Format: | Article |
| Language: | English |
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Elsevier
2021
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| 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 |
| _version_ | 1825814023871922176 |
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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 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. |
| first_indexed | 2024-03-06T12:52:41Z |
| format | Article |
| id | UMPir32338 |
| institution | Universiti Malaysia Pahang |
| language | English |
| last_indexed | 2024-03-06T12:52:41Z |
| publishDate | 2021 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | UMPir323382021-11-05T04:10:02Z 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. (Published) https://doi.org/10.1016/j.matcom.2020.10.028 https://doi.org/10.1016/j.matcom.2020.10.028 |
| 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 |
| title | 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_short | 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 |
| topic | QA Mathematics |
| 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 |
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