Numerical study for periodical delay differential equations using Runge-Kutta with trigonometric interpolation
A trigonometrically fitted diagonally implicit two-derivative Runge–Kutta method (TFDITDRK) is used for the numerical integration of first-order delay differential equations (DDEs) which possesses oscillatory solutions. Using the trigonometrically fitted property, a three-stage fifth-order diagonall...
| Main Authors: | , , , |
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| Format: | Article |
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Springer
2022
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| Online Access: | http://psasir.upm.edu.my/id/eprint/102346/ |
| _version_ | 1848863779159277568 |
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| author | Senu, Norazak Ahmad, Nur Amirah Othman, Mohamed Ibrahim, Zarina Bibi |
| author_facet | Senu, Norazak Ahmad, Nur Amirah Othman, Mohamed Ibrahim, Zarina Bibi |
| author_sort | Senu, Norazak |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | A trigonometrically fitted diagonally implicit two-derivative Runge–Kutta method (TFDITDRK) is used for the numerical integration of first-order delay differential equations (DDEs) which possesses oscillatory solutions. Using the trigonometrically fitted property, a three-stage fifth-order diagonally implicit two- derivative Runge–Kutta (DITDRK) method is derived. Here, we employed trigonometric interpolation for the approximation of the delay term. The curves of efficiency based on the log of maximum errors against the log of function evaluations and the CPU time spent to perform the integration are plotted, which then clearly illustrated the superiority of the trigonometrically fitted DITDRK method in comparison with its original method and other existing diagonally implicit Runge–Kutta (DIRK) methods. |
| first_indexed | 2025-11-15T13:38:20Z |
| format | Article |
| id | upm-102346 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T13:38:20Z |
| publishDate | 2022 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1023462023-05-22T08:10:39Z http://psasir.upm.edu.my/id/eprint/102346/ Numerical study for periodical delay differential equations using Runge-Kutta with trigonometric interpolation Senu, Norazak Ahmad, Nur Amirah Othman, Mohamed Ibrahim, Zarina Bibi A trigonometrically fitted diagonally implicit two-derivative Runge–Kutta method (TFDITDRK) is used for the numerical integration of first-order delay differential equations (DDEs) which possesses oscillatory solutions. Using the trigonometrically fitted property, a three-stage fifth-order diagonally implicit two- derivative Runge–Kutta (DITDRK) method is derived. Here, we employed trigonometric interpolation for the approximation of the delay term. The curves of efficiency based on the log of maximum errors against the log of function evaluations and the CPU time spent to perform the integration are plotted, which then clearly illustrated the superiority of the trigonometrically fitted DITDRK method in comparison with its original method and other existing diagonally implicit Runge–Kutta (DIRK) methods. Springer 2022-12-24 Article PeerReviewed Senu, Norazak and Ahmad, Nur Amirah and Othman, Mohamed and Ibrahim, Zarina Bibi (2022) Numerical study for periodical delay differential equations using Runge-Kutta with trigonometric interpolation. Computational and Applied Mathematics, 41. art. no. 25. pp. 1-20. ISSN 2238-3603; ESSN: 1807-0302 https://link.springer.com/article/10.1007/s40314-021-01728-8 10.1007/s40314-021-01728-8 |
| spellingShingle | Senu, Norazak Ahmad, Nur Amirah Othman, Mohamed Ibrahim, Zarina Bibi Numerical study for periodical delay differential equations using Runge-Kutta with trigonometric interpolation |
| title | Numerical study for periodical delay differential equations using Runge-Kutta with trigonometric interpolation |
| title_full | Numerical study for periodical delay differential equations using Runge-Kutta with trigonometric interpolation |
| title_fullStr | Numerical study for periodical delay differential equations using Runge-Kutta with trigonometric interpolation |
| title_full_unstemmed | Numerical study for periodical delay differential equations using Runge-Kutta with trigonometric interpolation |
| title_short | Numerical study for periodical delay differential equations using Runge-Kutta with trigonometric interpolation |
| title_sort | numerical study for periodical delay differential equations using runge-kutta with trigonometric interpolation |
| url | http://psasir.upm.edu.my/id/eprint/102346/ http://psasir.upm.edu.my/id/eprint/102346/ http://psasir.upm.edu.my/id/eprint/102346/ |