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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/10395/1/22%20Fudziah%20Ismail.pdf
http://journalarticle.ukm.my/10395/
http://www.ukm.my/jsm/english_journals/vol45num11_2016/contentsVol45num11_2016.html
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spelling my-ukm.journal.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
institution Universiti Kebangsaan Malaysia
building Perpustakaan Tun Sri Lanang Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Kebangsaan Malaysia
content_source UKM Journal Article Repository
url_provider http://journalarticle.ukm.my/
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/10395/1/22%20Fudziah%20Ismail.pdf
http://journalarticle.ukm.my/10395/
http://www.ukm.my/jsm/english_journals/vol45num11_2016/contentsVol45num11_2016.html
_version_ 1643738108539174912
score 13.211869

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