Third-order explicit two-step Runge-Kutta-Nyström method for solving second-order ordinary differential equations
A two-stage explicit two-step Runge-Kutta-Nyström (TSRKN) method is constructed for the numerical integration of special second-order IVPs. Algebraic order conditions of the method are obtained and third-order method is derived. A standard set of test problems are tested and comparisons on the numer...
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| Format: | Conference or Workshop Item |
| Language: | English |
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AIP Publishing LLC
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/57217/ http://psasir.upm.edu.my/id/eprint/57217/1/Third-order%20explicit%20two-step%20Runge-Kutta-Nystr%C3%B6m%20method%20for%20solving%20second-order%20ordinary%20differential%20equations.pdf |
| _version_ | 1848853303515938816 |
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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 two-stage explicit two-step Runge-Kutta-Nyström (TSRKN) method is constructed for the numerical integration of special second-order IVPs. Algebraic order conditions of the method are obtained and third-order method is derived. A standard set of test problems are tested and comparisons on the numerical results are made with existing Runge-Kutta-Nyström (RKN) and Runge-Kutta (RK) methods of the same order using constant step size. The numerical results show's its clear advantage in terms of function evaluation. |
| first_indexed | 2025-11-15T10:51:50Z |
| format | Conference or Workshop Item |
| id | upm-57217 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T10:51:50Z |
| publishDate | 2013 |
| publisher | AIP Publishing LLC |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-572172017-09-26T03:42:50Z http://psasir.upm.edu.my/id/eprint/57217/ Third-order explicit two-step Runge-Kutta-Nyström method for solving second-order ordinary differential equations Md Ariffin, Latifah Senu, Norazak Suleiman, Mohamed A two-stage explicit two-step Runge-Kutta-Nyström (TSRKN) method is constructed for the numerical integration of special second-order IVPs. Algebraic order conditions of the method are obtained and third-order method is derived. A standard set of test problems are tested and comparisons on the numerical results are made with existing Runge-Kutta-Nyström (RKN) and Runge-Kutta (RK) methods of the same order using constant step size. The numerical results show's its clear advantage in terms of function evaluation. AIP Publishing LLC 2013 Conference or Workshop Item PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/57217/1/Third-order%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 (2013) Third-order explicit two-step Runge-Kutta-Nyström method for solving second-order ordinary differential equations. In: International Conference on Mathematical Sciences and Statistics 2013 (ICMSS2013), 5-7 Feb. 2013, Kuala Lumpur, Malaysia. (pp. 326-329). 10.1063/1.4823929 |
| spellingShingle | Md Ariffin, Latifah Senu, Norazak Suleiman, Mohamed Third-order explicit two-step Runge-Kutta-Nyström method for solving second-order ordinary differential equations |
| title | Third-order explicit two-step Runge-Kutta-Nyström method for solving second-order ordinary differential equations |
| title_full | Third-order explicit two-step Runge-Kutta-Nyström method for solving second-order ordinary differential equations |
| title_fullStr | Third-order explicit two-step Runge-Kutta-Nyström method for solving second-order ordinary differential equations |
| title_full_unstemmed | Third-order explicit two-step Runge-Kutta-Nyström method for solving second-order ordinary differential equations |
| title_short | Third-order explicit two-step Runge-Kutta-Nyström method for solving second-order ordinary differential equations |
| title_sort | third-order explicit two-step runge-kutta-nyström method for solving second-order ordinary differential equations |
| url | http://psasir.upm.edu.my/id/eprint/57217/ http://psasir.upm.edu.my/id/eprint/57217/ http://psasir.upm.edu.my/id/eprint/57217/1/Third-order%20explicit%20two-step%20Runge-Kutta-Nystr%C3%B6m%20method%20for%20solving%20second-order%20ordinary%20differential%20equations.pdf |