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Efficient frequency-dependent coefficients of explicit improved two-derivative Runge-Kutta type methods for solving third order IVPs

This study aims to propose sixth-order two-derivative improved Runge-Kutta type methods adopted with exponentially-fitting and trigonometrically-fitting techniques for integrating a special type of third-order ordinary differential equation in the form u'''(t)=f(t,u(t),u'(t)). Th...

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Main Authors: Chien, Lee Khai, Senu, Norazak, Ahmadian, Ali, Ibrahim, Siti Nur Iqmal
Format: Article
Language:English
Published: Universiti Putra Malaysia Press 2023
Online Access:http://psasir.upm.edu.my/id/eprint/107629/1/10%20JST-3669-2022.pdf
http://psasir.upm.edu.my/id/eprint/107629/
http://www.pertanika.upm.edu.my/pjst/browse/regular-issue?article=JST-3669-2022
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spelling my.upm.eprints.1076292024-09-09T03:50:28Z http://psasir.upm.edu.my/id/eprint/107629/ Efficient frequency-dependent coefficients of explicit improved two-derivative Runge-Kutta type methods for solving third order IVPs Chien, Lee Khai Senu, Norazak Ahmadian, Ali Ibrahim, Siti Nur Iqmal This study aims to propose sixth-order two-derivative improved Runge-Kutta type methods adopted with exponentially-fitting and trigonometrically-fitting techniques for integrating a special type of third-order ordinary differential equation in the form u'''(t)=f(t,u(t),u'(t)). The procedure of constructing order conditions comprised of a few previous steps, k-i for third-order two-derivative Runge-Kutta-type methods, has been outlined. These methods are developed through the idea of integrating initial value problems exactly with a numerical solution in the form of linear composition of the set functions eѡt and e-ѡtfor exponentially fitted and eiѡt and e-iѡt for trigonometrically-fitted with ѡ ϵ R. Parameters of two-derivative Runge-Kutta type method are adapted into principle frequency of exponential and oscillatory problems to construct the proposed methods. Error analysis of proposed methods is analysed, and the computational efficiency of proposed methods is demonstrated in numerical experiments compared to other existing numerical methods for integrating third-order ordinary differential equations with an exponential and periodic solution. Universiti Putra Malaysia Press 2023-03-20 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/107629/1/10%20JST-3669-2022.pdf Chien, Lee Khai and Senu, Norazak and Ahmadian, Ali and Ibrahim, Siti Nur Iqmal (2023) Efficient frequency-dependent coefficients of explicit improved two-derivative Runge-Kutta type methods for solving third order IVPs. Pertanika Journal of Science and Technology, 31 (2). pp. 843-873. ISSN 0128-7680; ESSN: 2231-8526 http://www.pertanika.upm.edu.my/pjst/browse/regular-issue?article=JST-3669-2022 10.47836/pjst.31.2.10
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/
language English
description This study aims to propose sixth-order two-derivative improved Runge-Kutta type methods adopted with exponentially-fitting and trigonometrically-fitting techniques for integrating a special type of third-order ordinary differential equation in the form u'''(t)=f(t,u(t),u'(t)). The procedure of constructing order conditions comprised of a few previous steps, k-i for third-order two-derivative Runge-Kutta-type methods, has been outlined. These methods are developed through the idea of integrating initial value problems exactly with a numerical solution in the form of linear composition of the set functions eѡt and e-ѡtfor exponentially fitted and eiѡt and e-iѡt for trigonometrically-fitted with ѡ ϵ R. Parameters of two-derivative Runge-Kutta type method are adapted into principle frequency of exponential and oscillatory problems to construct the proposed methods. Error analysis of proposed methods is analysed, and the computational efficiency of proposed methods is demonstrated in numerical experiments compared to other existing numerical methods for integrating third-order ordinary differential equations with an exponential and periodic solution.
format Article
author Chien, Lee Khai
Senu, Norazak
Ahmadian, Ali
Ibrahim, Siti Nur Iqmal
spellingShingle Chien, Lee Khai
Senu, Norazak
Ahmadian, Ali
Ibrahim, Siti Nur Iqmal
Efficient frequency-dependent coefficients of explicit improved two-derivative Runge-Kutta type methods for solving third order IVPs
author_facet Chien, Lee Khai
Senu, Norazak
Ahmadian, Ali
Ibrahim, Siti Nur Iqmal
author_sort Chien, Lee Khai
title Efficient frequency-dependent coefficients of explicit improved two-derivative Runge-Kutta type methods for solving third order IVPs
title_short Efficient frequency-dependent coefficients of explicit improved two-derivative Runge-Kutta type methods for solving third order IVPs
title_full Efficient frequency-dependent coefficients of explicit improved two-derivative Runge-Kutta type methods for solving third order IVPs
title_fullStr Efficient frequency-dependent coefficients of explicit improved two-derivative Runge-Kutta type methods for solving third order IVPs
title_full_unstemmed Efficient frequency-dependent coefficients of explicit improved two-derivative Runge-Kutta type methods for solving third order IVPs
title_sort efficient frequency-dependent coefficients of explicit improved two-derivative runge-kutta type methods for solving third order ivps
publisher Universiti Putra Malaysia Press
publishDate 2023
url http://psasir.upm.edu.my/id/eprint/107629/1/10%20JST-3669-2022.pdf
http://psasir.upm.edu.my/id/eprint/107629/
http://www.pertanika.upm.edu.my/pjst/browse/regular-issue?article=JST-3669-2022
_version_ 1811685961816342528
score 13.2442

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