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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...

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التفاصيل البيبلوغرافية
المؤلفون الرئيسيون: Senu, Norazak, Ahmad, Nur Amirah, Othman, Mohamed, Ibrahim, Zarina Bibi
التنسيق: مقال
منشور في: Springer 2022
الوصول للمادة أونلاين:http://psasir.upm.edu.my/id/eprint/102346/
https://link.springer.com/article/10.1007/s40314-021-01728-8
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id my.upm.eprints.102346
record_format eprints
spelling my.upm.eprints.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
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
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.
format Article
author Senu, Norazak
Ahmad, Nur Amirah
Othman, Mohamed
Ibrahim, Zarina Bibi
spellingShingle Senu, Norazak
Ahmad, Nur Amirah
Othman, Mohamed
Ibrahim, Zarina Bibi
Numerical study for periodical delay differential equations using Runge-Kutta with trigonometric interpolation
author_facet Senu, Norazak
Ahmad, Nur Amirah
Othman, Mohamed
Ibrahim, Zarina Bibi
author_sort Senu, Norazak
title 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_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_sort numerical study for periodical delay differential equations using runge-kutta with trigonometric interpolation
publisher Springer
publishDate 2022
url http://psasir.upm.edu.my/id/eprint/102346/
https://link.springer.com/article/10.1007/s40314-021-01728-8
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score 13.251813

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