Semi implicit hybrid methods with higher order dispersion for solving oscillatory problems
We constructed three two-step semi-implicit hybrid methods (SIHMs) for solving oscillatory second order ordinary differential equations (ODEs). The first two methods are three-stage fourth-order and three-stage fifth-order with dispersion order six and zero dissipation. The third is a four-stage fif...
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| Format: | Article |
| Language: | English |
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Hindawi Publishing Corporation
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/30209/ http://psasir.upm.edu.my/id/eprint/30209/1/30209.pdf |
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| author | Ahmad, Sufia Zulfa Ismail, Fudziah Senu, Norazak Suleiman, Mohamed |
| author_facet | Ahmad, Sufia Zulfa Ismail, Fudziah Senu, Norazak Suleiman, Mohamed |
| author_sort | Ahmad, Sufia Zulfa |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | We constructed three two-step semi-implicit hybrid methods (SIHMs) for solving oscillatory second order ordinary differential equations (ODEs). The first two methods are three-stage fourth-order and three-stage fifth-order with dispersion order six and zero dissipation. The third is a four-stage fifth-order method with dispersion order eight and dissipation order five. Numerical results show that SIHMs are more accurate as compared to the existing hybrid methods, Runge-Kutta Nyström (RKN) and Runge-Kutta (RK) methods of the same order and Diagonally Implicit Runge-Kutta Nyström (DIRKN) method of the same stage. The intervals of absolute stability or periodicity of SIHM for ODE are also presented. |
| first_indexed | 2025-11-15T09:05:29Z |
| format | Article |
| id | upm-30209 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T09:05:29Z |
| publishDate | 2013 |
| publisher | Hindawi Publishing Corporation |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-302092017-10-19T05:53:30Z http://psasir.upm.edu.my/id/eprint/30209/ Semi implicit hybrid methods with higher order dispersion for solving oscillatory problems Ahmad, Sufia Zulfa Ismail, Fudziah Senu, Norazak Suleiman, Mohamed We constructed three two-step semi-implicit hybrid methods (SIHMs) for solving oscillatory second order ordinary differential equations (ODEs). The first two methods are three-stage fourth-order and three-stage fifth-order with dispersion order six and zero dissipation. The third is a four-stage fifth-order method with dispersion order eight and dissipation order five. Numerical results show that SIHMs are more accurate as compared to the existing hybrid methods, Runge-Kutta Nyström (RKN) and Runge-Kutta (RK) methods of the same order and Diagonally Implicit Runge-Kutta Nyström (DIRKN) method of the same stage. The intervals of absolute stability or periodicity of SIHM for ODE are also presented. Hindawi Publishing Corporation 2013 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/30209/1/30209.pdf Ahmad, Sufia Zulfa and Ismail, Fudziah and Senu, Norazak and Suleiman, Mohamed (2013) Semi implicit hybrid methods with higher order dispersion for solving oscillatory problems. Abstract and Applied Analysis, 2013. art. no. 136961. pp. 1-10. ISSN 1085-3375; ESSN: 1687-0409 https://www.hindawi.com/journals/aaa/2013/136961/abs/ 10.1155/2013/136961 |
| spellingShingle | Ahmad, Sufia Zulfa Ismail, Fudziah Senu, Norazak Suleiman, Mohamed Semi implicit hybrid methods with higher order dispersion for solving oscillatory problems |
| title | Semi implicit hybrid methods with higher order dispersion for solving oscillatory problems |
| title_full | Semi implicit hybrid methods with higher order dispersion for solving oscillatory problems |
| title_fullStr | Semi implicit hybrid methods with higher order dispersion for solving oscillatory problems |
| title_full_unstemmed | Semi implicit hybrid methods with higher order dispersion for solving oscillatory problems |
| title_short | Semi implicit hybrid methods with higher order dispersion for solving oscillatory problems |
| title_sort | semi implicit hybrid methods with higher order dispersion for solving oscillatory problems |
| url | http://psasir.upm.edu.my/id/eprint/30209/ http://psasir.upm.edu.my/id/eprint/30209/ http://psasir.upm.edu.my/id/eprint/30209/ http://psasir.upm.edu.my/id/eprint/30209/1/30209.pdf |