Integration for special third-order ordinary differential equations using improved Runge-Kutta direct method
In this paper, we derive an explicit four stage fifth-order Improved Runge-Kutta (IRKD) method for numerical integration of special third-order ordinary differential equation. The method proposed here is two-step in nature and require less number of stages per step compared with the existing Runge-K...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Faculty of Science, University of Malaya
2015
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| Online Access: | http://psasir.upm.edu.my/id/eprint/51961/ http://psasir.upm.edu.my/id/eprint/51961/1/Integration%20for%20special%20third-order%20ordinary%20differential%20equations%20using%20improved%20Runge-Kutta%20direct%20method.pdf |
| _version_ | 1848851975794327552 |
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| author | Hussain, Kasim Abbas Ismail, Fudziah Senu, Norazak Rabiei, Faranak Ibrahim, Rabha Waell |
| author_facet | Hussain, Kasim Abbas Ismail, Fudziah Senu, Norazak Rabiei, Faranak Ibrahim, Rabha Waell |
| author_sort | Hussain, Kasim Abbas |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this paper, we derive an explicit four stage fifth-order Improved Runge-Kutta (IRKD) method for numerical integration of special third-order ordinary differential equation. The method proposed here is two-step in nature and require less number of stages per step compared with the existing Runge-Kutta (RK) method. The stability polynomial of the IRKD method is presented. Numerical results are given to illustrate the efficiency of the proposed method compared to the RK method and direct Runge-Kutta (RKD) method for solving special third-order ordinary differential equations. |
| first_indexed | 2025-11-15T10:30:44Z |
| format | Article |
| id | upm-51961 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T10:30:44Z |
| publishDate | 2015 |
| publisher | Faculty of Science, University of Malaya |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-519612017-05-04T04:33:45Z http://psasir.upm.edu.my/id/eprint/51961/ Integration for special third-order ordinary differential equations using improved Runge-Kutta direct method Hussain, Kasim Abbas Ismail, Fudziah Senu, Norazak Rabiei, Faranak Ibrahim, Rabha Waell In this paper, we derive an explicit four stage fifth-order Improved Runge-Kutta (IRKD) method for numerical integration of special third-order ordinary differential equation. The method proposed here is two-step in nature and require less number of stages per step compared with the existing Runge-Kutta (RK) method. The stability polynomial of the IRKD method is presented. Numerical results are given to illustrate the efficiency of the proposed method compared to the RK method and direct Runge-Kutta (RKD) method for solving special third-order ordinary differential equations. Faculty of Science, University of Malaya 2015 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/51961/1/Integration%20for%20special%20third-order%20ordinary%20differential%20equations%20using%20improved%20Runge-Kutta%20direct%20method.pdf Hussain, Kasim Abbas and Ismail, Fudziah and Senu, Norazak and Rabiei, Faranak and Ibrahim, Rabha Waell (2015) Integration for special third-order ordinary differential equations using improved Runge-Kutta direct method. Malaysian Journal of Science, 34 (2). pp. 172-179. ISSN 0126-7906 http://e-journal.um.edu.my/publish/MJS/925-1141 |
| spellingShingle | Hussain, Kasim Abbas Ismail, Fudziah Senu, Norazak Rabiei, Faranak Ibrahim, Rabha Waell Integration for special third-order ordinary differential equations using improved Runge-Kutta direct method |
| title | Integration for special third-order ordinary differential equations using improved Runge-Kutta direct method |
| title_full | Integration for special third-order ordinary differential equations using improved Runge-Kutta direct method |
| title_fullStr | Integration for special third-order ordinary differential equations using improved Runge-Kutta direct method |
| title_full_unstemmed | Integration for special third-order ordinary differential equations using improved Runge-Kutta direct method |
| title_short | Integration for special third-order ordinary differential equations using improved Runge-Kutta direct method |
| title_sort | integration for special third-order ordinary differential equations using improved runge-kutta direct method |
| url | http://psasir.upm.edu.my/id/eprint/51961/ http://psasir.upm.edu.my/id/eprint/51961/ http://psasir.upm.edu.my/id/eprint/51961/1/Integration%20for%20special%20third-order%20ordinary%20differential%20equations%20using%20improved%20Runge-Kutta%20direct%20method.pdf |