Implicit two-point block method for solving fourth order initial value problem directly with application
This paper proposes an implicit block method with two-point to directly solve the fourth-order Initial Value Problems (IVPs). The implicit block method is derived by adopting Hermite interpolating polynomial as the basis function, incorporating the first derivative of to enhance the solution’s accu...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi
2020
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| Online Access: | http://psasir.upm.edu.my/id/eprint/89313/ http://psasir.upm.edu.my/id/eprint/89313/1/BLOCK.pdf |
| _version_ | 1848860822805151744 |
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| author | Allogmany, Reem Ayed Ismail, Fudziah Abdul Majid, Zanariah Ibrahim, Zarina Bibi |
| author_facet | Allogmany, Reem Ayed Ismail, Fudziah Abdul Majid, Zanariah Ibrahim, Zarina Bibi |
| author_sort | Allogmany, Reem Ayed |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | This paper proposes an implicit block method with two-point to directly solve the fourth-order Initial Value Problems (IVPs). The implicit block method is derived by adopting Hermite interpolating polynomial as the basis function, incorporating the first derivative of to enhance the solution’s accuracy. A block formulation is presented to acquire the numerical approximation at two points simultaneously. The introduced method’s basic properties, including order, zero stability, and convergence, are presented. Numerical experiments are carried out to verify the accuracy and efficiency of the proposed method compared with those of the several existing methods. Application in ship dynamics is also presented which yield impressive results for the proposed two-point block method. |
| first_indexed | 2025-11-15T12:51:21Z |
| format | Article |
| id | upm-89313 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T12:51:21Z |
| publishDate | 2020 |
| publisher | Hindawi |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-893132021-09-03T08:41:27Z http://psasir.upm.edu.my/id/eprint/89313/ Implicit two-point block method for solving fourth order initial value problem directly with application Allogmany, Reem Ayed Ismail, Fudziah Abdul Majid, Zanariah Ibrahim, Zarina Bibi This paper proposes an implicit block method with two-point to directly solve the fourth-order Initial Value Problems (IVPs). The implicit block method is derived by adopting Hermite interpolating polynomial as the basis function, incorporating the first derivative of to enhance the solution’s accuracy. A block formulation is presented to acquire the numerical approximation at two points simultaneously. The introduced method’s basic properties, including order, zero stability, and convergence, are presented. Numerical experiments are carried out to verify the accuracy and efficiency of the proposed method compared with those of the several existing methods. Application in ship dynamics is also presented which yield impressive results for the proposed two-point block method. Hindawi 2020 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/89313/1/BLOCK.pdf Allogmany, Reem Ayed and Ismail, Fudziah and Abdul Majid, Zanariah and Ibrahim, Zarina Bibi (2020) Implicit two-point block method for solving fourth order initial value problem directly with application. Mathematical Problems in Engineering, 2020. art. no. 6351279. pp. 1-16. ISSN 1024-123X; ESSN: 1563-5147 https://www.hindawi.com/journals/mpe/2020/6351279/ 10.1155/2020/6351279 |
| spellingShingle | Allogmany, Reem Ayed Ismail, Fudziah Abdul Majid, Zanariah Ibrahim, Zarina Bibi Implicit two-point block method for solving fourth order initial value problem directly with application |
| title | Implicit two-point block method for solving fourth order initial value problem directly with application |
| title_full | Implicit two-point block method for solving fourth order initial value problem directly with application |
| title_fullStr | Implicit two-point block method for solving fourth order initial value problem directly with application |
| title_full_unstemmed | Implicit two-point block method for solving fourth order initial value problem directly with application |
| title_short | Implicit two-point block method for solving fourth order initial value problem directly with application |
| title_sort | implicit two-point block method for solving fourth order initial value problem directly with application |
| url | http://psasir.upm.edu.my/id/eprint/89313/ http://psasir.upm.edu.my/id/eprint/89313/ http://psasir.upm.edu.my/id/eprint/89313/ http://psasir.upm.edu.my/id/eprint/89313/1/BLOCK.pdf |