Solving directly special fourth-order ordinary differential equations using Runge-Kutta type method
In this paper, an explicit Runge–Kutta method for solving directly fourth-order ordinary differential equations (ODEs) is constructed and denoted as (RKFD). We present a relevant-colored tree theory and the associated B-series theory for the order conditions. Based on the order conditions a three-st...
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| Format: | Article |
| Language: | English |
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Elsevier BV
2016
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| Online Access: | http://psasir.upm.edu.my/id/eprint/53850/ http://psasir.upm.edu.my/id/eprint/53850/1/Solving%20directly%20special%20fourth-order%20ordinary%20differential%20equations%20using%20Runge%E2%80%93Kutta%20type%20method.pdf |
| _version_ | 1848852391636500480 |
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| author | Hussain, Kasim Ismail, Fudziah Senu, Norazak |
| author_facet | Hussain, Kasim Ismail, Fudziah Senu, Norazak |
| author_sort | Hussain, Kasim |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this paper, an explicit Runge–Kutta method for solving directly fourth-order ordinary differential equations (ODEs) is constructed and denoted as (RKFD). We present a relevant-colored tree theory and the associated B-series theory for the order conditions. Based on the order conditions a three-stage fourth-order RKFD method and a three-stage fifth-order RKFD method are constructed. Numerical illustrations are presented to show the efficiency of the new RKFD methods by comparing them with other existing Runge–Kutta Nyström (RKN) and Runge–Kutta (RK) methods in the scientific literature after converting the problem into a system of second order ODEs and a system of first order ODEs respectively. |
| first_indexed | 2025-11-15T10:37:20Z |
| format | Article |
| id | upm-53850 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T10:37:20Z |
| publishDate | 2016 |
| publisher | Elsevier BV |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-538502018-02-13T08:20:50Z http://psasir.upm.edu.my/id/eprint/53850/ Solving directly special fourth-order ordinary differential equations using Runge-Kutta type method Hussain, Kasim Ismail, Fudziah Senu, Norazak In this paper, an explicit Runge–Kutta method for solving directly fourth-order ordinary differential equations (ODEs) is constructed and denoted as (RKFD). We present a relevant-colored tree theory and the associated B-series theory for the order conditions. Based on the order conditions a three-stage fourth-order RKFD method and a three-stage fifth-order RKFD method are constructed. Numerical illustrations are presented to show the efficiency of the new RKFD methods by comparing them with other existing Runge–Kutta Nyström (RKN) and Runge–Kutta (RK) methods in the scientific literature after converting the problem into a system of second order ODEs and a system of first order ODEs respectively. Elsevier BV 2016-11 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/53850/1/Solving%20directly%20special%20fourth-order%20ordinary%20differential%20equations%20using%20Runge%E2%80%93Kutta%20type%20method.pdf Hussain, Kasim and Ismail, Fudziah and Senu, Norazak (2016) Solving directly special fourth-order ordinary differential equations using Runge-Kutta type method. Journal of Computational and Applied Mathematics, 306. pp. 179-199. ISSN 0377-0427; ESSN: 1879-1778 https://www.sciencedirect.com/science/article/pii/S0377042716301662#! 10.1016/j.cam.2016.04.002 |
| spellingShingle | Hussain, Kasim Ismail, Fudziah Senu, Norazak Solving directly special fourth-order ordinary differential equations using Runge-Kutta type method |
| title | Solving directly special fourth-order ordinary differential equations using Runge-Kutta type method |
| title_full | Solving directly special fourth-order ordinary differential equations using Runge-Kutta type method |
| title_fullStr | Solving directly special fourth-order ordinary differential equations using Runge-Kutta type method |
| title_full_unstemmed | Solving directly special fourth-order ordinary differential equations using Runge-Kutta type method |
| title_short | Solving directly special fourth-order ordinary differential equations using Runge-Kutta type method |
| title_sort | solving directly special fourth-order ordinary differential equations using runge-kutta type method |
| url | http://psasir.upm.edu.my/id/eprint/53850/ http://psasir.upm.edu.my/id/eprint/53850/ http://psasir.upm.edu.my/id/eprint/53850/ http://psasir.upm.edu.my/id/eprint/53850/1/Solving%20directly%20special%20fourth-order%20ordinary%20differential%20equations%20using%20Runge%E2%80%93Kutta%20type%20method.pdf |