High-order exponentially fitted and trigonometrically fitted explicit two-derivative Runge–Kutta-type methods for solving third-order oscillatory problems
Three stage sixth-order exponentially fitted and trigonometrically fitted explicit two-derivative Runge–Kutta-type methods are proposed for solving u'''(t) = f(t, u(t), u'(t)). The idea of construction is based on linear composition of the set functions ewt and e-wt for exponenti...
| Main Authors: | , , , |
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| Format: | Article |
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Springer Medizin
2021
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| Online Access: | http://psasir.upm.edu.my/id/eprint/97528/ |
| _version_ | 1848862623610699776 |
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| author | Lee, Khai Chien Senu, Norazak Ahmadian, Ali Ibrahim, Siti Nur Iqmal |
| author_facet | Lee, Khai Chien Senu, Norazak Ahmadian, Ali Ibrahim, Siti Nur Iqmal |
| author_sort | Lee, Khai Chien |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | Three stage sixth-order exponentially fitted and trigonometrically fitted explicit two-derivative Runge–Kutta-type methods are proposed for solving u'''(t) = f(t, u(t), u'(t)). The idea of construction is based on linear composition of the set functions ewt and e-wt for exponentially fitted and eiwt and e-iwt for trigonometrically fitted with weR to integrate initial value problems. The selected coefficients of two-derivative Runge–Kutta-type method are modified to depend on the principle frequency of the numerical problems to construct exponentially fitted and trigonometrically fitted Runge–Kutta-type direct methods, denoted as EFTDRKT6 and TFTDRKT6 methods. The numerical experiments illustrate competence of the new exponentially fitted and trigonometrically fitted method compared to existing methods for solving special type third-order ordinary differential equations with initial value problems. |
| first_indexed | 2025-11-15T13:19:58Z |
| format | Article |
| id | upm-97528 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T13:19:58Z |
| publishDate | 2021 |
| publisher | Springer Medizin |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-975282024-08-19T02:13:44Z http://psasir.upm.edu.my/id/eprint/97528/ High-order exponentially fitted and trigonometrically fitted explicit two-derivative Runge–Kutta-type methods for solving third-order oscillatory problems Lee, Khai Chien Senu, Norazak Ahmadian, Ali Ibrahim, Siti Nur Iqmal Three stage sixth-order exponentially fitted and trigonometrically fitted explicit two-derivative Runge–Kutta-type methods are proposed for solving u'''(t) = f(t, u(t), u'(t)). The idea of construction is based on linear composition of the set functions ewt and e-wt for exponentially fitted and eiwt and e-iwt for trigonometrically fitted with weR to integrate initial value problems. The selected coefficients of two-derivative Runge–Kutta-type method are modified to depend on the principle frequency of the numerical problems to construct exponentially fitted and trigonometrically fitted Runge–Kutta-type direct methods, denoted as EFTDRKT6 and TFTDRKT6 methods. The numerical experiments illustrate competence of the new exponentially fitted and trigonometrically fitted method compared to existing methods for solving special type third-order ordinary differential equations with initial value problems. Springer Medizin 2021-07-23 Article PeerReviewed Lee, Khai Chien and Senu, Norazak and Ahmadian, Ali and Ibrahim, Siti Nur Iqmal (2021) High-order exponentially fitted and trigonometrically fitted explicit two-derivative Runge–Kutta-type methods for solving third-order oscillatory problems. Mathematical Sciences, 16 (3). pp. 281-297. ISSN 2008-1359; EISSN: 2251-7456 https://link.springer.com/article/10.1007/s40096-021-00420-6 10.1007/s40096-021-00420-6 |
| spellingShingle | Lee, Khai Chien Senu, Norazak Ahmadian, Ali Ibrahim, Siti Nur Iqmal High-order exponentially fitted and trigonometrically fitted explicit two-derivative Runge–Kutta-type methods for solving third-order oscillatory problems |
| title | High-order exponentially fitted and trigonometrically fitted explicit two-derivative Runge–Kutta-type methods for solving third-order oscillatory problems |
| title_full | High-order exponentially fitted and trigonometrically fitted explicit two-derivative Runge–Kutta-type methods for solving third-order oscillatory problems |
| title_fullStr | High-order exponentially fitted and trigonometrically fitted explicit two-derivative Runge–Kutta-type methods for solving third-order oscillatory problems |
| title_full_unstemmed | High-order exponentially fitted and trigonometrically fitted explicit two-derivative Runge–Kutta-type methods for solving third-order oscillatory problems |
| title_short | High-order exponentially fitted and trigonometrically fitted explicit two-derivative Runge–Kutta-type methods for solving third-order oscillatory problems |
| title_sort | high-order exponentially fitted and trigonometrically fitted explicit two-derivative runge–kutta-type methods for solving third-order oscillatory problems |
| url | http://psasir.upm.edu.my/id/eprint/97528/ http://psasir.upm.edu.my/id/eprint/97528/ http://psasir.upm.edu.my/id/eprint/97528/ |