Embedded diagonally implicit Runge–Kutta–Nystrom 4(3) pair for solving special second-order IVPs
In this paper, third-order 3-stage diagonally implicit Runge–Kutta–Nystrom method embedded in fourth-order 4-stage for solving special second-order initial value problems is constructed. The method has the property of minimized local truncation error as well as the last row of the coefficient matrix...
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| Format: | Article |
| Language: | English English |
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Elsevier
2007
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| Online Access: | http://psasir.upm.edu.my/id/eprint/7666/ http://psasir.upm.edu.my/id/eprint/7666/1/Embedded%20diagonally%20implicit%20Runge.pdf |
| _version_ | 1848840659657555968 |
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| author | Al-Khasawneh, Raed Ali Ismail, Fudziah Suleiman, Mohamed |
| author_facet | Al-Khasawneh, Raed Ali Ismail, Fudziah Suleiman, Mohamed |
| author_sort | Al-Khasawneh, Raed Ali |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this paper, third-order 3-stage diagonally implicit Runge–Kutta–Nystrom method embedded in fourth-order 4-stage for solving special second-order initial value problems is constructed. The method has the property of minimized local truncation error as well as the last row of the coefficient matrix is equal to the vector output. The stability of the method is investigated and a standard set of test problems are tested upon and comparisons on the numerical results are made when the same set of test problems are reduced to first-order system and solved using existing Runge–Kutta method. The results clearly shown the advantage and the efficiency of the new method |
| first_indexed | 2025-11-15T07:30:52Z |
| format | Article |
| id | upm-7666 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-15T07:30:52Z |
| publishDate | 2007 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-76662015-12-08T04:27:28Z http://psasir.upm.edu.my/id/eprint/7666/ Embedded diagonally implicit Runge–Kutta–Nystrom 4(3) pair for solving special second-order IVPs Al-Khasawneh, Raed Ali Ismail, Fudziah Suleiman, Mohamed In this paper, third-order 3-stage diagonally implicit Runge–Kutta–Nystrom method embedded in fourth-order 4-stage for solving special second-order initial value problems is constructed. The method has the property of minimized local truncation error as well as the last row of the coefficient matrix is equal to the vector output. The stability of the method is investigated and a standard set of test problems are tested upon and comparisons on the numerical results are made when the same set of test problems are reduced to first-order system and solved using existing Runge–Kutta method. The results clearly shown the advantage and the efficiency of the new method Elsevier 2007 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/7666/1/Embedded%20diagonally%20implicit%20Runge.pdf Al-Khasawneh, Raed Ali and Ismail, Fudziah and Suleiman, Mohamed (2007) Embedded diagonally implicit Runge–Kutta–Nystrom 4(3) pair for solving special second-order IVPs. Applied Mathematics and Computation, 190 (2). pp. 1803-1814. ISSN 0096-3003 http://dx.doi.org/10.1016/j.amc.2007.02.067 10.1016/j.amc.2007.02.067 English |
| spellingShingle | Al-Khasawneh, Raed Ali Ismail, Fudziah Suleiman, Mohamed Embedded diagonally implicit Runge–Kutta–Nystrom 4(3) pair for solving special second-order IVPs |
| title | Embedded diagonally implicit Runge–Kutta–Nystrom 4(3) pair for solving special second-order IVPs
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| title_full | Embedded diagonally implicit Runge–Kutta–Nystrom 4(3) pair for solving special second-order IVPs
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| title_fullStr | Embedded diagonally implicit Runge–Kutta–Nystrom 4(3) pair for solving special second-order IVPs
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| title_full_unstemmed | Embedded diagonally implicit Runge–Kutta–Nystrom 4(3) pair for solving special second-order IVPs
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| title_short | Embedded diagonally implicit Runge–Kutta–Nystrom 4(3) pair for solving special second-order IVPs
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| title_sort | embedded diagonally implicit runge–kutta–nystrom 4(3) pair for solving special second-order ivps |
| url | http://psasir.upm.edu.my/id/eprint/7666/ http://psasir.upm.edu.my/id/eprint/7666/ http://psasir.upm.edu.my/id/eprint/7666/ http://psasir.upm.edu.my/id/eprint/7666/1/Embedded%20diagonally%20implicit%20Runge.pdf |