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...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2020
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| Online Access: | http://psasir.upm.edu.my/id/eprint/86938/1/Numerical%20study%20of%20third-order%20ordinary%20differential%20equations.pdf |
| _version_ | 1825952290830286848 |
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| author | Lee, Khai Chien Senu, Norazak Ahmadian, Ali Ibrahim, Siti Nur Iqmal Baleanu, D. |
| author_facet | Lee, Khai Chien Senu, Norazak Ahmadian, Ali Ibrahim, Siti Nur Iqmal Baleanu, D. |
| author_sort | Lee, Khai Chien |
| collection | UPM |
| 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. |
| first_indexed | 2024-03-06T10:42:43Z |
| format | Article |
| id | upm.eprints-86938 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T10:42:43Z |
| publishDate | 2020 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | 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 |
| 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 |
| title | 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_short | 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 |
| url | http://psasir.upm.edu.my/id/eprint/86938/1/Numerical%20study%20of%20third-order%20ordinary%20differential%20equations.pdf |
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