A trigonometrically adapted 6(4) explicit Runge–Kutta–Nyström pair to solve oscillating systems
In this study, a trigonometrically adapted 6(4) explicit Runge–Kutta–Nyström (RKN) pair with six stages is formulated, considering a previous method developed by El-Mikkawy and Rahmo. The obtained adapted pair integrates exactly the usual test equation: y" = w2y . The local truncation error of...
| Main Authors: | , , , , , |
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| Format: | Article |
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John Wiley & Sons
2022
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| Online Access: | http://psasir.upm.edu.my/id/eprint/100484/ |
| _version_ | 1848863335466926080 |
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| author | Ahmed Demba, Musa Ramos, Higinio Kumam, Poom Watthayu, Wiboonsak Senu, Norazak Ahmed, Idris |
| author_facet | Ahmed Demba, Musa Ramos, Higinio Kumam, Poom Watthayu, Wiboonsak Senu, Norazak Ahmed, Idris |
| author_sort | Ahmed Demba, Musa |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this study, a trigonometrically adapted 6(4) explicit Runge–Kutta–Nyström (RKN) pair with six stages is formulated, considering a previous method developed by El-Mikkawy and Rahmo. The obtained adapted pair integrates exactly the usual test equation: y" = w2y . The local truncation error of the new method is presented, showing that the algebraic order of the original method is maintained. The periodicity interval of the new method is computed, showing that the developed method is “almost” P-stable. The numerical examples considered clearly show the superiority of the new developed embedded pair over other RKN methods of algebraic orders 6(4) with six stages appeared in the literature. |
| first_indexed | 2025-11-15T13:31:17Z |
| format | Article |
| id | upm-100484 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T13:31:17Z |
| publishDate | 2022 |
| publisher | John Wiley & Sons |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1004842023-11-23T08:46:39Z http://psasir.upm.edu.my/id/eprint/100484/ A trigonometrically adapted 6(4) explicit Runge–Kutta–Nyström pair to solve oscillating systems Ahmed Demba, Musa Ramos, Higinio Kumam, Poom Watthayu, Wiboonsak Senu, Norazak Ahmed, Idris In this study, a trigonometrically adapted 6(4) explicit Runge–Kutta–Nyström (RKN) pair with six stages is formulated, considering a previous method developed by El-Mikkawy and Rahmo. The obtained adapted pair integrates exactly the usual test equation: y" = w2y . The local truncation error of the new method is presented, showing that the algebraic order of the original method is maintained. The periodicity interval of the new method is computed, showing that the developed method is “almost” P-stable. The numerical examples considered clearly show the superiority of the new developed embedded pair over other RKN methods of algebraic orders 6(4) with six stages appeared in the literature. John Wiley & Sons 2022-07-03 Article PeerReviewed Ahmed Demba, Musa and Ramos, Higinio and Kumam, Poom and Watthayu, Wiboonsak and Senu, Norazak and Ahmed, Idris (2022) A trigonometrically adapted 6(4) explicit Runge–Kutta–Nyström pair to solve oscillating systems. Mathematical Methods in the Applied Sciences, 46 (1). 560 - 578. ISSN 0170-4214; ESSN: 1099-1476 https://onlinelibrary.wiley.com/doi/abs/10.1002/mma.8528 10.1002/mma.8528 |
| spellingShingle | Ahmed Demba, Musa Ramos, Higinio Kumam, Poom Watthayu, Wiboonsak Senu, Norazak Ahmed, Idris A trigonometrically adapted 6(4) explicit Runge–Kutta–Nyström pair to solve oscillating systems |
| title | A trigonometrically adapted 6(4) explicit Runge–Kutta–Nyström pair to solve oscillating systems |
| title_full | A trigonometrically adapted 6(4) explicit Runge–Kutta–Nyström pair to solve oscillating systems |
| title_fullStr | A trigonometrically adapted 6(4) explicit Runge–Kutta–Nyström pair to solve oscillating systems |
| title_full_unstemmed | A trigonometrically adapted 6(4) explicit Runge–Kutta–Nyström pair to solve oscillating systems |
| title_short | A trigonometrically adapted 6(4) explicit Runge–Kutta–Nyström pair to solve oscillating systems |
| title_sort | trigonometrically adapted 6(4) explicit runge–kutta–nyström pair to solve oscillating systems |
| url | http://psasir.upm.edu.my/id/eprint/100484/ http://psasir.upm.edu.my/id/eprint/100484/ http://psasir.upm.edu.my/id/eprint/100484/ |