A sixth-order RKFD method with four-stage for directly solving special fourth-order ODEs
In this article, the general form of Runge-Kutta method for directly solving a special fourth- order ordinary differential equations denoted as RKFD method is given. The order conditions up to order seven are derived, based on the order conditions, we construct a new explicit four-stage sixth-order...
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| Format: | Article |
| Language: | English |
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Universiti Kebangsaan Malaysia
2016
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| Online Access: | http://psasir.upm.edu.my/id/eprint/54939/ http://psasir.upm.edu.my/id/eprint/54939/1/A%20sixth-order%20RKFD%20method%20with%20four-stage%20for%20directly%20solving%20special%20fourth-order%20.pdf |
| _version_ | 1848852671756238848 |
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| author | Ismail, Fudziah Hussain, Kasim Senu, Norazak |
| author_facet | Ismail, Fudziah Hussain, Kasim Senu, Norazak |
| author_sort | Ismail, Fudziah |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this article, the general form of Runge-Kutta method for directly solving a special fourth- order ordinary differential equations denoted as RKFD method is given. The order conditions up to order seven are derived, based on the order conditions, we construct a new explicit four-stage sixth-order RKFD method denoted as RKFD6 method. Zero-stability of the method is proven. Comparisons are made using the existing Runge–Kutta methods after the problems are reduced to a system of first order ordinary differential equations. Numerical results are presented to illustrate the efficiency and competency of the new method. |
| first_indexed | 2025-11-15T10:41:47Z |
| format | Article |
| id | upm-54939 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T10:41:47Z |
| publishDate | 2016 |
| publisher | Universiti Kebangsaan Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-549392018-06-12T08:20:37Z http://psasir.upm.edu.my/id/eprint/54939/ A sixth-order RKFD method with four-stage for directly solving special fourth-order ODEs Ismail, Fudziah Hussain, Kasim Senu, Norazak In this article, the general form of Runge-Kutta method for directly solving a special fourth- order ordinary differential equations denoted as RKFD method is given. The order conditions up to order seven are derived, based on the order conditions, we construct a new explicit four-stage sixth-order RKFD method denoted as RKFD6 method. Zero-stability of the method is proven. Comparisons are made using the existing Runge–Kutta methods after the problems are reduced to a system of first order ordinary differential equations. Numerical results are presented to illustrate the efficiency and competency of the new method. Universiti Kebangsaan Malaysia 2016 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/54939/1/A%20sixth-order%20RKFD%20method%20with%20four-stage%20for%20directly%20solving%20special%20fourth-order%20.pdf Ismail, Fudziah and Hussain, Kasim and Senu, Norazak (2016) A sixth-order RKFD method with four-stage for directly solving special fourth-order ODEs. Sains Malaysiana, 11 (45). pp. 1747-1754. ISSN 0026-6039 |
| spellingShingle | Ismail, Fudziah Hussain, Kasim Senu, Norazak A sixth-order RKFD method with four-stage for directly solving special fourth-order ODEs |
| title | A sixth-order RKFD method with four-stage for directly solving special fourth-order ODEs |
| title_full | A sixth-order RKFD method with four-stage for directly solving special fourth-order ODEs |
| title_fullStr | A sixth-order RKFD method with four-stage for directly solving special fourth-order ODEs |
| title_full_unstemmed | A sixth-order RKFD method with four-stage for directly solving special fourth-order ODEs |
| title_short | A sixth-order RKFD method with four-stage for directly solving special fourth-order ODEs |
| title_sort | sixth-order rkfd method with four-stage for directly solving special fourth-order odes |
| url | http://psasir.upm.edu.my/id/eprint/54939/ http://psasir.upm.edu.my/id/eprint/54939/1/A%20sixth-order%20RKFD%20method%20with%20four-stage%20for%20directly%20solving%20special%20fourth-order%20.pdf |