An embedded explicit Runge-Kutta-Nystrom method for solving oscillatory problems
A new pair of embedded explicit Runge–Kutta–Nyström (RKN) methods is developed to integrate second-order differential equations of the form q00=f(t,q) where the solution is oscillatory. The embedded formula has dispersion order eight and dissipation order seven for the fifth-order formula. The cost...
| Main Authors: | , , |
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| Format: | Article |
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Institute of Physics Publishing
2009
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| Online Access: | http://psasir.upm.edu.my/id/eprint/13027/ |
| _version_ | 1848841998730002432 |
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| author | Senu, Norazak Suleiman, Mohamed Ismail, Fudziah |
| author_facet | Senu, Norazak Suleiman, Mohamed Ismail, Fudziah |
| author_sort | Senu, Norazak |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | A new pair of embedded explicit Runge–Kutta–Nyström (RKN) methods is developed to integrate second-order differential equations of the form q00=f(t,q) where the solution is
oscillatory. The embedded formula has dispersion order eight and dissipation order seven for the fifth-order formula. The cost for this pair is four function evaluations at each step of integration. Numerical comparisons with several codes in the scientific literature such as RKN5(4)D, RKN5(4)B,RKN4(3)G and DOPRI5 show the efficiency of the new method developed. |
| first_indexed | 2025-11-15T07:52:09Z |
| format | Article |
| id | upm-13027 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T07:52:09Z |
| publishDate | 2009 |
| publisher | Institute of Physics Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-130272015-07-29T07:37:58Z http://psasir.upm.edu.my/id/eprint/13027/ An embedded explicit Runge-Kutta-Nystrom method for solving oscillatory problems Senu, Norazak Suleiman, Mohamed Ismail, Fudziah A new pair of embedded explicit Runge–Kutta–Nyström (RKN) methods is developed to integrate second-order differential equations of the form q00=f(t,q) where the solution is oscillatory. The embedded formula has dispersion order eight and dissipation order seven for the fifth-order formula. The cost for this pair is four function evaluations at each step of integration. Numerical comparisons with several codes in the scientific literature such as RKN5(4)D, RKN5(4)B,RKN4(3)G and DOPRI5 show the efficiency of the new method developed. Institute of Physics Publishing 2009-07 Article PeerReviewed Senu, Norazak and Suleiman, Mohamed and Ismail, Fudziah (2009) An embedded explicit Runge-Kutta-Nystrom method for solving oscillatory problems. Physica Scripta, 80 (1). art. no. 015005. pp. 1-7. ISSN 0031-8949; ESSN: 1402-4896 http://iopscience.iop.org/1402-4896/80/1/015005 10.1088/0031-8949/80/01/015005 |
| spellingShingle | Senu, Norazak Suleiman, Mohamed Ismail, Fudziah An embedded explicit Runge-Kutta-Nystrom method for solving oscillatory problems |
| title | An embedded explicit Runge-Kutta-Nystrom method for solving oscillatory problems |
| title_full | An embedded explicit Runge-Kutta-Nystrom method for solving oscillatory problems |
| title_fullStr | An embedded explicit Runge-Kutta-Nystrom method for solving oscillatory problems |
| title_full_unstemmed | An embedded explicit Runge-Kutta-Nystrom method for solving oscillatory problems |
| title_short | An embedded explicit Runge-Kutta-Nystrom method for solving oscillatory problems |
| title_sort | embedded explicit runge-kutta-nystrom method for solving oscillatory problems |
| url | http://psasir.upm.edu.my/id/eprint/13027/ http://psasir.upm.edu.my/id/eprint/13027/ http://psasir.upm.edu.my/id/eprint/13027/ |