A three-stage explicit two-step Runge-Kutta-Nyström method for solving second-order ordinary differential equations
A three-stage explicit two-step Runge-Kutta-Nyström (TSRKN) method is developed for the numerical integration of special second-order ordinary differential equations. Algebraic order conditions of the method are obtained and fourth-order method is derived. The second-order initial value problems of...
| Main Authors: | , , |
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| Format: | Conference or Workshop Item |
| Language: | English |
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AIP Publishing LLC
2012
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| Online Access: | http://psasir.upm.edu.my/id/eprint/57454/ http://psasir.upm.edu.my/id/eprint/57454/1/A%20three-stage%20explicit%20two-step%20Runge-Kutta-Nystr%C3%B6m%20method%20for%20solving%20second-order%20ordinary%20differential%20equations.pdf |
| _version_ | 1848853370848149504 |
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| author | Md Ariffin, Latifah Senu, Norazak Suleiman, Mohamed |
| author_facet | Md Ariffin, Latifah Senu, Norazak Suleiman, Mohamed |
| author_sort | Md Ariffin, Latifah |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | A three-stage explicit two-step Runge-Kutta-Nyström (TSRKN) method is developed for the numerical integration of special second-order ordinary differential equations. Algebraic order conditions of the method are obtained and fourth-order method is derived. The second-order initial value problems of ordinary differential equations (ODEs) are solved directly using TSRKN and Runge-Kutta-Nyström (RKN) methods. The problems were then reduced to first-order system when solved by Runge-Kutta (RK) method. Numerical comparison of this new method with the existing RK and RKN methods of the same order using constant step size are carried out to illustrate its efficiency and it shows that the new method has clear advantage in terms of function evaluation. |
| first_indexed | 2025-11-15T10:52:54Z |
| format | Conference or Workshop Item |
| id | upm-57454 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T10:52:54Z |
| publishDate | 2012 |
| publisher | AIP Publishing LLC |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-574542017-09-27T10:46:50Z http://psasir.upm.edu.my/id/eprint/57454/ A three-stage explicit two-step Runge-Kutta-Nyström method for solving second-order ordinary differential equations Md Ariffin, Latifah Senu, Norazak Suleiman, Mohamed A three-stage explicit two-step Runge-Kutta-Nyström (TSRKN) method is developed for the numerical integration of special second-order ordinary differential equations. Algebraic order conditions of the method are obtained and fourth-order method is derived. The second-order initial value problems of ordinary differential equations (ODEs) are solved directly using TSRKN and Runge-Kutta-Nyström (RKN) methods. The problems were then reduced to first-order system when solved by Runge-Kutta (RK) method. Numerical comparison of this new method with the existing RK and RKN methods of the same order using constant step size are carried out to illustrate its efficiency and it shows that the new method has clear advantage in terms of function evaluation. AIP Publishing LLC 2012 Conference or Workshop Item PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/57454/1/A%20three-stage%20explicit%20two-step%20Runge-Kutta-Nystr%C3%B6m%20method%20for%20solving%20second-order%20ordinary%20differential%20equations.pdf Md Ariffin, Latifah and Senu, Norazak and Suleiman, Mohamed (2012) A three-stage explicit two-step Runge-Kutta-Nyström method for solving second-order ordinary differential equations. In: 20th National Symposium on Mathematical Sciences (SKSM20), 18-20 Dec. 2012, Palm Garden Hotel, Putrajaya, Malaysia. (pp. 323-329). 10.1063/1.4801142 |
| spellingShingle | Md Ariffin, Latifah Senu, Norazak Suleiman, Mohamed A three-stage explicit two-step Runge-Kutta-Nyström method for solving second-order ordinary differential equations |
| title | A three-stage explicit two-step Runge-Kutta-Nyström method for solving second-order ordinary differential equations |
| title_full | A three-stage explicit two-step Runge-Kutta-Nyström method for solving second-order ordinary differential equations |
| title_fullStr | A three-stage explicit two-step Runge-Kutta-Nyström method for solving second-order ordinary differential equations |
| title_full_unstemmed | A three-stage explicit two-step Runge-Kutta-Nyström method for solving second-order ordinary differential equations |
| title_short | A three-stage explicit two-step Runge-Kutta-Nyström method for solving second-order ordinary differential equations |
| title_sort | three-stage explicit two-step runge-kutta-nyström method for solving second-order ordinary differential equations |
| url | http://psasir.upm.edu.my/id/eprint/57454/ http://psasir.upm.edu.my/id/eprint/57454/ http://psasir.upm.edu.my/id/eprint/57454/1/A%20three-stage%20explicit%20two-step%20Runge-Kutta-Nystr%C3%B6m%20method%20for%20solving%20second-order%20ordinary%20differential%20equations.pdf |