Phase fitted and amplification fitted of Runge-Kutta-Fehlberg method of order 4(5) for solving oscillatory problems
In this paper, the proposed phase fitted and amplification fitted of the Runge-Kutta-Fehlberg method were derived on the basis of existing method of 4(5) order to solve ordinary differential equations with oscillatory solutions. The recent method has null phase-lag and zero dissipation properties. T...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Published: |
College of Science for Women/ University of Baghdad
2020
|
| _version_ | 1796981810435981312 |
|---|---|
| author | Salih, Mohammed M. Ismail, Fudziah Senu, Norazak |
| author_facet | Salih, Mohammed M. Ismail, Fudziah Senu, Norazak |
| author_sort | Salih, Mohammed M. |
| collection | UPM |
| description | In this paper, the proposed phase fitted and amplification fitted of the Runge-Kutta-Fehlberg method were derived on the basis of existing method of 4(5) order to solve ordinary differential equations with oscillatory solutions. The recent method has null phase-lag and zero dissipation properties. The phase-lag or dispersion error is the angle between the real solution and the approximate solution. While the dissipation is the distance of the numerical solution from the basic periodic solution. Many of problems are tested over a long interval, and the numerical results have shown that the present method is more precise than the 4(5) Runge-Kutta-Fehlberg method. |
| first_indexed | 2024-03-06T10:43:05Z |
| format | Article |
| id | upm.eprints-87142 |
| institution | Universiti Putra Malaysia |
| last_indexed | 2024-03-06T10:43:05Z |
| publishDate | 2020 |
| publisher | College of Science for Women/ University of Baghdad |
| record_format | dspace |
| spelling | upm.eprints-871422023-01-26T01:23:57Z http://psasir.upm.edu.my/id/eprint/87142/ Phase fitted and amplification fitted of Runge-Kutta-Fehlberg method of order 4(5) for solving oscillatory problems Salih, Mohammed M. Ismail, Fudziah Senu, Norazak In this paper, the proposed phase fitted and amplification fitted of the Runge-Kutta-Fehlberg method were derived on the basis of existing method of 4(5) order to solve ordinary differential equations with oscillatory solutions. The recent method has null phase-lag and zero dissipation properties. The phase-lag or dispersion error is the angle between the real solution and the approximate solution. While the dissipation is the distance of the numerical solution from the basic periodic solution. Many of problems are tested over a long interval, and the numerical results have shown that the present method is more precise than the 4(5) Runge-Kutta-Fehlberg method. College of Science for Women/ University of Baghdad 2020-06-22 Article PeerReviewed Salih, Mohammed M. and Ismail, Fudziah and Senu, Norazak (2020) Phase fitted and amplification fitted of Runge-Kutta-Fehlberg method of order 4(5) for solving oscillatory problems. Baghdad Science Journal, 17. 689 - 693. ISSN 2078-8665; ESSN: 2411-7986 https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/4024 10.21123/bsj.2020.17.2(SI).0689 |
| spellingShingle | Salih, Mohammed M. Ismail, Fudziah Senu, Norazak Phase fitted and amplification fitted of Runge-Kutta-Fehlberg method of order 4(5) for solving oscillatory problems |
| title | Phase fitted and amplification fitted of Runge-Kutta-Fehlberg method of order 4(5) for solving oscillatory problems |
| title_full | Phase fitted and amplification fitted of Runge-Kutta-Fehlberg method of order 4(5) for solving oscillatory problems |
| title_fullStr | Phase fitted and amplification fitted of Runge-Kutta-Fehlberg method of order 4(5) for solving oscillatory problems |
| title_full_unstemmed | Phase fitted and amplification fitted of Runge-Kutta-Fehlberg method of order 4(5) for solving oscillatory problems |
| title_short | Phase fitted and amplification fitted of Runge-Kutta-Fehlberg method of order 4(5) for solving oscillatory problems |
| title_sort | phase fitted and amplification fitted of runge kutta fehlberg method of order 4 5 for solving oscillatory problems |
| work_keys_str_mv | AT salihmohammedm phasefittedandamplificationfittedofrungekuttafehlbergmethodoforder45forsolvingoscillatoryproblems AT ismailfudziah phasefittedandamplificationfittedofrungekuttafehlbergmethodoforder45forsolvingoscillatoryproblems AT senunorazak phasefittedandamplificationfittedofrungekuttafehlbergmethodoforder45forsolvingoscillatoryproblems |