Efficient two-derivative Runge-Kutta-Nyström methods for solving general second-order ordinary differential equations y"(x) = f(x,y,y')
This paper proposes and investigates a special class of explicit Runge-Kutta-Nyström (RKN) methods for problems in the form y'' (x) = f (x,y, y') including third derivatives and denoted as STDRKN. The methods involve one evaluation of second derivative and many evaluations of third d...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Hindawi
2018
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| Online Access: | http://psasir.upm.edu.my/id/eprint/72537/ http://psasir.upm.edu.my/id/eprint/72537/1/Efficient%20two%20derivative%20.pdf |
| _version_ | 1848857142686121984 |
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| author | Salama, Tahani Mohamed Senu, Norazak Ibrahim, Zarina Bibi Nik Long, Nik Mohd Asri |
| author_facet | Salama, Tahani Mohamed Senu, Norazak Ibrahim, Zarina Bibi Nik Long, Nik Mohd Asri |
| author_sort | Salama, Tahani Mohamed |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | This paper proposes and investigates a special class of explicit Runge-Kutta-Nyström (RKN) methods for problems in the form y'' (x) = f (x,y, y') including third derivatives and denoted as STDRKN. The methods involve one evaluation of second derivative and many evaluations of third derivative per step. In this study, methods with two and three stages of orders four and five, respectively, are presented. The stability property of the methods is discussed. Numerical experiments have clearly shown the accuracy and the efficiency of the new methods. |
| first_indexed | 2025-11-15T11:52:51Z |
| format | Article |
| id | upm-72537 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T11:52:51Z |
| publishDate | 2018 |
| publisher | Hindawi |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-725372020-10-22T11:06:16Z http://psasir.upm.edu.my/id/eprint/72537/ Efficient two-derivative Runge-Kutta-Nyström methods for solving general second-order ordinary differential equations y"(x) = f(x,y,y') Salama, Tahani Mohamed Senu, Norazak Ibrahim, Zarina Bibi Nik Long, Nik Mohd Asri This paper proposes and investigates a special class of explicit Runge-Kutta-Nyström (RKN) methods for problems in the form y'' (x) = f (x,y, y') including third derivatives and denoted as STDRKN. The methods involve one evaluation of second derivative and many evaluations of third derivative per step. In this study, methods with two and three stages of orders four and five, respectively, are presented. The stability property of the methods is discussed. Numerical experiments have clearly shown the accuracy and the efficiency of the new methods. Hindawi 2018 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/72537/1/Efficient%20two%20derivative%20.pdf Salama, Tahani Mohamed and Senu, Norazak and Ibrahim, Zarina Bibi and Nik Long, Nik Mohd Asri (2018) Efficient two-derivative Runge-Kutta-Nyström methods for solving general second-order ordinary differential equations y"(x) = f(x,y,y'). Discrete Dynamics in Nature and Society, 2018. art. no. 2393015. pp. 1-10. ISSN 1026-0226; ESSN: 1607-887X https://www.hindawi.com/journals/ddns/2018/2393015/ 10.1155/2018/2393015 |
| spellingShingle | Salama, Tahani Mohamed Senu, Norazak Ibrahim, Zarina Bibi Nik Long, Nik Mohd Asri Efficient two-derivative Runge-Kutta-Nyström methods for solving general second-order ordinary differential equations y"(x) = f(x,y,y') |
| title | Efficient two-derivative Runge-Kutta-Nyström methods for solving general second-order ordinary differential equations y"(x) = f(x,y,y') |
| title_full | Efficient two-derivative Runge-Kutta-Nyström methods for solving general second-order ordinary differential equations y"(x) = f(x,y,y') |
| title_fullStr | Efficient two-derivative Runge-Kutta-Nyström methods for solving general second-order ordinary differential equations y"(x) = f(x,y,y') |
| title_full_unstemmed | Efficient two-derivative Runge-Kutta-Nyström methods for solving general second-order ordinary differential equations y"(x) = f(x,y,y') |
| title_short | Efficient two-derivative Runge-Kutta-Nyström methods for solving general second-order ordinary differential equations y"(x) = f(x,y,y') |
| title_sort | efficient two-derivative runge-kutta-nyström methods for solving general second-order ordinary differential equations y"(x) = f(x,y,y') |
| url | http://psasir.upm.edu.my/id/eprint/72537/ http://psasir.upm.edu.my/id/eprint/72537/ http://psasir.upm.edu.my/id/eprint/72537/ http://psasir.upm.edu.my/id/eprint/72537/1/Efficient%20two%20derivative%20.pdf |