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Numerical study of third-order ordinary differential equations using a new class of two derivative Runge-Kutta type methods

This study introduces new special two-derivative Runge-Kutta type (STDRKT) methods involving the fourth derivative of the solution for solving third-order ordinary differential equations. In this regards, rooted tree theory and the corresponding B-series theory is proposed to derive order conditions...

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Main Authors: Lee, Khai Chien, Senu, Norazak, Ahmadian, Ali, Ibrahim, Siti Nur Iqmal, Baleanu, D.
Format: Article
Language:English
Published: Elsevier 2020
Online Access:http://psasir.upm.edu.my/id/eprint/86938/1/Numerical%20study%20of%20third-order%20ordinary%20differential%20equations.pdf
http://psasir.upm.edu.my/id/eprint/86938/
https://www.sciencedirect.com/journal/alexandria-engineering-journal/vol/59/issue/4
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spelling my.upm.eprints.869382022-01-10T04:13:40Z http://psasir.upm.edu.my/id/eprint/86938/ Numerical study of third-order ordinary differential equations using a new class of two derivative Runge-Kutta type methods Lee, Khai Chien Senu, Norazak Ahmadian, Ali Ibrahim, Siti Nur Iqmal Baleanu, D. This study introduces new special two-derivative Runge-Kutta type (STDRKT) methods involving the fourth derivative of the solution for solving third-order ordinary differential equations. In this regards, rooted tree theory and the corresponding B-series theory is proposed to derive order conditions for STDRKT methods. Besides, explicit two-stages fifth order and three-stages sixth order STDRKT methods are derived and stability,consistency and convergence of STDRKT methods are analysed in details. Accuracy and effectiveness of the proposed techniques are validated by a number of various test problems and compared to existing methods in the literature. Elsevier 2020-08 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/86938/1/Numerical%20study%20of%20third-order%20ordinary%20differential%20equations.pdf Lee, Khai Chien and Senu, Norazak and Ahmadian, Ali and Ibrahim, Siti Nur Iqmal and Baleanu, D. (2020) Numerical study of third-order ordinary differential equations using a new class of two derivative Runge-Kutta type methods. Alexandria Engineering Journal, 59 (4). 2449 - 2467. ISSN 1110-0168; ESSN: 2090-2670 https://www.sciencedirect.com/journal/alexandria-engineering-journal/vol/59/issue/4 10.1016/j.aej.2020.03.008
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 introduces new special two-derivative Runge-Kutta type (STDRKT) methods involving the fourth derivative of the solution for solving third-order ordinary differential equations. In this regards, rooted tree theory and the corresponding B-series theory is proposed to derive order conditions for STDRKT methods. Besides, explicit two-stages fifth order and three-stages sixth order STDRKT methods are derived and stability,consistency and convergence of STDRKT methods are analysed in details. Accuracy and effectiveness of the proposed techniques are validated by a number of various test problems and compared to existing methods in the literature.
format Article
author Lee, Khai Chien
Senu, Norazak
Ahmadian, Ali
Ibrahim, Siti Nur Iqmal
Baleanu, D.
spellingShingle Lee, Khai Chien
Senu, Norazak
Ahmadian, Ali
Ibrahim, Siti Nur Iqmal
Baleanu, D.
Numerical study of third-order ordinary differential equations using a new class of two derivative Runge-Kutta type methods
author_facet Lee, Khai Chien
Senu, Norazak
Ahmadian, Ali
Ibrahim, Siti Nur Iqmal
Baleanu, D.
author_sort Lee, Khai Chien
title Numerical study of third-order ordinary differential equations using a new class of two derivative Runge-Kutta type methods
title_short Numerical study of third-order ordinary differential equations using a new class of two derivative Runge-Kutta type methods
title_full Numerical study of third-order ordinary differential equations using a new class of two derivative Runge-Kutta type methods
title_fullStr Numerical study of third-order ordinary differential equations using a new class of two derivative Runge-Kutta type methods
title_full_unstemmed Numerical study of third-order ordinary differential equations using a new class of two derivative Runge-Kutta type methods
title_sort numerical study of third-order ordinary differential equations using a new class of two derivative runge-kutta type methods
publisher Elsevier
publishDate 2020
url http://psasir.upm.edu.my/id/eprint/86938/1/Numerical%20study%20of%20third-order%20ordinary%20differential%20equations.pdf
http://psasir.upm.edu.my/id/eprint/86938/
https://www.sciencedirect.com/journal/alexandria-engineering-journal/vol/59/issue/4
_version_ 1724075481235456000
score 13.160551

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