Exponentially-fitted Runge-Kutta Nystrom method of order three for solving oscillatory problems
In this paper the exponentially fitted explicit Runge-Kutta Nystrom method is proposed for solving special second-order ordinary differential equations where the solution is oscillatory. The exponentially fitting is based on given Runge-Kutta Nystrom (RKN) method of order three at a cost of three fu...
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| Format: | Article |
| Language: | English |
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Institute for Mathematical Research, Universiti Putra Malaysia
2014
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| Online Access: | http://psasir.upm.edu.my/id/eprint/39047/ http://psasir.upm.edu.my/id/eprint/39047/1/39047.pdf |
| _version_ | 1848849039195373568 |
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| author | Rabiei, Faranak Ismail, Fudziah Senu, Norazak |
| author_facet | Rabiei, Faranak Ismail, Fudziah Senu, Norazak |
| author_sort | Rabiei, Faranak |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this paper the exponentially fitted explicit Runge-Kutta Nystrom method is proposed for solving special second-order ordinary differential equations where the solution is oscillatory. The exponentially fitting is based on given Runge-Kutta Nystrom (RKN) method of order three at a cost of three function evaluations per step. Here, we also developed the trigonometrically-fitted RKN method for solving initial value problems with oscillating solutions. The numerical results compared with the existing explicit RKN method of order three which indicates that the exponentially fitted explicit Runge-Kutta Nystrom method is more efficient than the classical RKN method. |
| first_indexed | 2025-11-15T09:44:03Z |
| format | Article |
| id | upm-39047 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T09:44:03Z |
| publishDate | 2014 |
| publisher | Institute for Mathematical Research, Universiti Putra Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-390472015-09-01T11:29:10Z http://psasir.upm.edu.my/id/eprint/39047/ Exponentially-fitted Runge-Kutta Nystrom method of order three for solving oscillatory problems Rabiei, Faranak Ismail, Fudziah Senu, Norazak In this paper the exponentially fitted explicit Runge-Kutta Nystrom method is proposed for solving special second-order ordinary differential equations where the solution is oscillatory. The exponentially fitting is based on given Runge-Kutta Nystrom (RKN) method of order three at a cost of three function evaluations per step. Here, we also developed the trigonometrically-fitted RKN method for solving initial value problems with oscillating solutions. The numerical results compared with the existing explicit RKN method of order three which indicates that the exponentially fitted explicit Runge-Kutta Nystrom method is more efficient than the classical RKN method. Institute for Mathematical Research, Universiti Putra Malaysia 2014-10 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/39047/1/39047.pdf Rabiei, Faranak and Ismail, Fudziah and Senu, Norazak (2014) Exponentially-fitted Runge-Kutta Nystrom method of order three for solving oscillatory problems. Malaysian Journal of Mathematical Sciences, 8 (S). pp. 17-24. ISSN 1823-8343; ESSN: 2289-750X http://einspem.upm.edu.my/journal/fullpaper/vol8soct/2.%20Faranak%20Rabiei.pdf |
| spellingShingle | Rabiei, Faranak Ismail, Fudziah Senu, Norazak Exponentially-fitted Runge-Kutta Nystrom method of order three for solving oscillatory problems |
| title | Exponentially-fitted Runge-Kutta Nystrom method of order three for solving oscillatory problems |
| title_full | Exponentially-fitted Runge-Kutta Nystrom method of order three for solving oscillatory problems |
| title_fullStr | Exponentially-fitted Runge-Kutta Nystrom method of order three for solving oscillatory problems |
| title_full_unstemmed | Exponentially-fitted Runge-Kutta Nystrom method of order three for solving oscillatory problems |
| title_short | Exponentially-fitted Runge-Kutta Nystrom method of order three for solving oscillatory problems |
| title_sort | exponentially-fitted runge-kutta nystrom method of order three for solving oscillatory problems |
| url | http://psasir.upm.edu.my/id/eprint/39047/ http://psasir.upm.edu.my/id/eprint/39047/ http://psasir.upm.edu.my/id/eprint/39047/1/39047.pdf |