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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Main Authors:	Fudziah Ismail, Hussain, Kasim, Norazak Senu
Format:	Article
Language:	English
Published:	Penerbit Universiti Kebangsaan Malaysia 2016
Online Access:	http://journalarticle.ukm.my/10395/ http://journalarticle.ukm.my/10395/ http://journalarticle.ukm.my/10395/1/22%20Fudziah%20Ismail.pdf

id	ukm-10395
recordtype	eprints
spelling	ukm-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
repository_type	Digital Repository
institution_category	Local University
institution	Universiti Kebangasaan Malaysia
building	UKM Institutional Repository
collection	Online Access
language	English
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.
format	Article
author	Fudziah Ismail, Hussain, Kasim Norazak Senu,
spellingShingle	Fudziah Ismail, Hussain, Kasim Norazak Senu, A sixth-order RKFD method with four-stage for directly solving special fourth-order ODEs
author_facet	Fudziah Ismail, Hussain, Kasim Norazak Senu,
author_sort	Fudziah Ismail,
title	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_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_sort	sixth-order rkfd method with four-stage for directly solving special fourth-order odes
publisher	Penerbit Universiti Kebangsaan Malaysia
publishDate	2016
url	http://journalarticle.ukm.my/10395/ http://journalarticle.ukm.my/10395/ http://journalarticle.ukm.my/10395/1/22%20Fudziah%20Ismail.pdf
first_indexed	2023-09-18T19:57:18Z
last_indexed	2023-09-18T19:57:18Z
_version_	1777406615070179328

A sixth-order RKFD method with four-stage for directly solving special fourth-order ODEs

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