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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| Published in | Mathematics and computers in simulation Vol. 182; pp. 411 - 427 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.04.2021
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0378-4754 1872-7166 |
| DOI | 10.1016/j.matcom.2020.10.028 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Bachok, Norfifah Ismail, Fudziah Abdul Majid, Zanariah Mohd Nasir, Nadirah |
| Author_xml | – sequence: 1 givenname: Nadirah surname: Mohd Nasir fullname: Mohd Nasir, Nadirah organization: Institute for Mathematical Research, Universiti Putra Malaysia, 43400, Serdang, Selangor, Malaysia – sequence: 2 givenname: Zanariah surname: Abdul Majid fullname: Abdul Majid, Zanariah email: am_zana@upm.edu.my organization: Institute for Mathematical Research, Universiti Putra Malaysia, 43400, Serdang, Selangor, Malaysia – sequence: 3 givenname: Fudziah surname: Ismail fullname: Ismail, Fudziah organization: Institute for Mathematical Research, Universiti Putra Malaysia, 43400, Serdang, Selangor, Malaysia – sequence: 4 givenname: Norfifah surname: Bachok fullname: Bachok, Norfifah organization: Institute for Mathematical Research, Universiti Putra Malaysia, 43400, Serdang, Selangor, Malaysia |
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| Cites_doi | 10.1007/s40819-018-0542-6 10.1016/j.matcom.2019.03.003 10.12988/ijma.2016.510266 10.5897/IJPS2013.4019 10.1016/j.cam.2020.112876 10.1007/s11075-010-9375-z 10.1080/0020716031000079572 10.1016/j.amc.2017.10.003 10.1007/s11075-010-9413-x 10.1080/00207169108804026 10.1109/ICMSAO.2011.5775503 10.18576/amis/100403 10.1016/j.amc.2015.08.129 10.1080/00207169908804816 10.1016/j.amc.2017.06.038 |
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| Keywords | Third-order differential equations Boundary value problems Robin boundary conditions Linear multistep method Shooting method |
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| SubjectTerms | Boundary value problems Linear multistep method Robin boundary conditions Shooting method Third-order differential equations |
| Title | Direct integration of the third-order two point and multipoint Robin type boundary value problems |
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