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...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Penerbit Universiti Kebangsaan Malaysia
2016
|
| Online Access: | http://journalarticle.ukm.my/10395/ http://journalarticle.ukm.my/10395/1/22%20Fudziah%20Ismail.pdf |
| _version_ | 1848812375787962368 |
|---|---|
| author | Fudziah Ismail, Hussain, Kasim Norazak Senu, |
| author_facet | Fudziah Ismail, Hussain, Kasim Norazak Senu, |
| author_sort | Fudziah Ismail, |
| building | UKM 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 | 2025-11-15T00:01:18Z |
| format | Article |
| id | oai:generic.eprints.org:10395 |
| institution | Universiti Kebangasaan Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T00:01:18Z |
| publishDate | 2016 |
| publisher | Penerbit Universiti Kebangsaan Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | oai:generic.eprints.org:103952017-05-22T00:11:34Z http://journalarticle.ukm.my/10395/ A sixth-order RKFD method with four-stage for directly solving special fourth-order ODEs Fudziah Ismail, Hussain, Kasim Norazak Senu, 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. Penerbit Universiti Kebangsaan Malaysia 2016-11 Article PeerReviewed application/pdf en http://journalarticle.ukm.my/10395/1/22%20Fudziah%20Ismail.pdf Fudziah Ismail, and Hussain, Kasim and Norazak Senu, (2016) A sixth-order RKFD method with four-stage for directly solving special fourth-order ODEs. Sains Malaysiana, 45 (11). pp. 1747-1754. ISSN 0126-6039 http://www.ukm.my/jsm/english_journals/vol45num11_2016/contentsVol45num11_2016.html |
| spellingShingle | Fudziah Ismail, Hussain, Kasim Norazak Senu, 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://journalarticle.ukm.my/10395/ http://journalarticle.ukm.my/10395/ http://journalarticle.ukm.my/10395/1/22%20Fudziah%20Ismail.pdf |