Runge-Kutta type methods for directly solving special fourth-order ordinary differential equations
A Runge-Kutta type method for directly solving special fourth-order ordinary differential equations (ODEs) which is denoted by RKFD method is constructed. The order conditions of RKFD method up to order five are derived; based on the order conditions, three-stage fourth- and fifth-order Runge-Kutta...
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| Format: | Article |
| Language: | English |
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Hindawi
2015
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| Online Access: | http://psasir.upm.edu.my/id/eprint/46211/ http://psasir.upm.edu.my/id/eprint/46211/1/Runge-Kutta%20type%20methods%20for%20directly%20solving%20special%20fourth-order%20ordinary%20differential%20equations.pdf |
| _version_ | 1848850616760139776 |
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| author | Hussain, Kasim Abbas Ismail, Fudziah Senu, Norazak |
| author_facet | Hussain, Kasim Abbas Ismail, Fudziah Senu, Norazak |
| author_sort | Hussain, Kasim Abbas |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | A Runge-Kutta type method for directly solving special fourth-order ordinary differential equations (ODEs) which is denoted by RKFD method is constructed. The order conditions of RKFD method up to order five are derived; based on the order conditions, three-stage fourth- and fifth-order Runge-Kutta type methods are constructed. Zero-stability of the RKFD method is proven. Numerical results obtained are compared with the existing Runge-Kutta methods in the scientific literature after reducing the problems into a system of first-order ODEs and solving them. Numerical results are presented to illustrate the robustness and competency of the new methods in terms of accuracy and number of function evaluations. |
| first_indexed | 2025-11-15T10:09:08Z |
| format | Article |
| id | upm-46211 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T10:09:08Z |
| publishDate | 2015 |
| publisher | Hindawi |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-462112022-05-31T20:53:30Z http://psasir.upm.edu.my/id/eprint/46211/ Runge-Kutta type methods for directly solving special fourth-order ordinary differential equations Hussain, Kasim Abbas Ismail, Fudziah Senu, Norazak A Runge-Kutta type method for directly solving special fourth-order ordinary differential equations (ODEs) which is denoted by RKFD method is constructed. The order conditions of RKFD method up to order five are derived; based on the order conditions, three-stage fourth- and fifth-order Runge-Kutta type methods are constructed. Zero-stability of the RKFD method is proven. Numerical results obtained are compared with the existing Runge-Kutta methods in the scientific literature after reducing the problems into a system of first-order ODEs and solving them. Numerical results are presented to illustrate the robustness and competency of the new methods in terms of accuracy and number of function evaluations. Hindawi 2015 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/46211/1/Runge-Kutta%20type%20methods%20for%20directly%20solving%20special%20fourth-order%20ordinary%20differential%20equations.pdf Hussain, Kasim Abbas and Ismail, Fudziah and Senu, Norazak (2015) Runge-Kutta type methods for directly solving special fourth-order ordinary differential equations. Mathematical Problems in Engineering, 2015. art. no. 893763. pp. 1-11. ISSN 1024-123X; ESSN: 1563-5147 https://www.hindawi.com/journals/mpe/2015/893763/ 10.1155/2015/893763 |
| spellingShingle | Hussain, Kasim Abbas Ismail, Fudziah Senu, Norazak Runge-Kutta type methods for directly solving special fourth-order ordinary differential equations |
| title | Runge-Kutta type methods for directly solving special fourth-order ordinary differential equations |
| title_full | Runge-Kutta type methods for directly solving special fourth-order ordinary differential equations |
| title_fullStr | Runge-Kutta type methods for directly solving special fourth-order ordinary differential equations |
| title_full_unstemmed | Runge-Kutta type methods for directly solving special fourth-order ordinary differential equations |
| title_short | Runge-Kutta type methods for directly solving special fourth-order ordinary differential equations |
| title_sort | runge-kutta type methods for directly solving special fourth-order ordinary differential equations |
| url | http://psasir.upm.edu.my/id/eprint/46211/ http://psasir.upm.edu.my/id/eprint/46211/ http://psasir.upm.edu.my/id/eprint/46211/ http://psasir.upm.edu.my/id/eprint/46211/1/Runge-Kutta%20type%20methods%20for%20directly%20solving%20special%20fourth-order%20ordinary%20differential%20equations.pdf |