Order-4 symmetrized runge-kutta methods for stiff problems (Kaedah Runge-Kutta Tersimetri Peringkat-4 untuk Masalah Kaku)

If a Runge-Kutta method having an asymptotic error expansion in the stepsize h is symmetric then it is characterised by an h2-expansion. Since elimination of the leading error terms in succession results in an increase in the order by two at a time, a symmetric method could therefore be suitable fo...

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Main Authors:	Robert P.K, Chan, Annie Gorgey
Format:	Article
Language:	English
Published:	Penerbit Universiti Kebangsaan Malaysia 2011
Online Access:	http://journalarticle.ukm.my/2890/ http://journalarticle.ukm.my/2890/ http://journalarticle.ukm.my/2890/1/jqma-7-1-05-gorgey.pdf

id	ukm-2890
recordtype	eprints
spelling	ukm-28902016-12-14T06:32:57Z http://journalarticle.ukm.my/2890/ Order-4 symmetrized runge-kutta methods for stiff problems (Kaedah Runge-Kutta Tersimetri Peringkat-4 untuk Masalah Kaku) Robert P.K, Chan, Annie Gorgey, If a Runge-Kutta method having an asymptotic error expansion in the stepsize h is symmetric then it is characterised by an h2-expansion. Since elimination of the leading error terms in succession results in an increase in the order by two at a time, a symmetric method could therefore be suitable for the construction of extrapolation methods. However, when order reduction occurs for stiff problems it needs to be suppressed before an appropriate extrapolation formula can be applied. This can be achieved by a process called symmetrization which is a composition of the symmetric method with an L-stable method known as a symmetrizer. The symmetrizer is constructed so as to preserve the h2-asymptotic error expansion. In this paper we consider symmetrization of the 2-stage Gauss and the 3-stage Lobatto IIIA methods of order 4. We show that these methods are more efficient when used with symmetrization. Extrapolation based on the symmetrized methods is therefore expected to give greater accuracy. We also show that the method with a higher stage order is more advantageous than one with a lower stage order for solving stiff problems. Penerbit Universiti Kebangsaan Malaysia 2011-07 Article PeerReviewed application/pdf en http://journalarticle.ukm.my/2890/1/jqma-7-1-05-gorgey.pdf Robert P.K, and Chan, and Annie Gorgey, (2011) Order-4 symmetrized runge-kutta methods for stiff problems (Kaedah Runge-Kutta Tersimetri Peringkat-4 untuk Masalah Kaku). Journal of Quality Measurement and Analysis, 7 (1). pp. 53-66. ISSN 1823-5670 http://www.ukm.my/~ppsmfst/jqma
repository_type	Digital Repository
institution_category	Local University
institution	Universiti Kebangasaan Malaysia
building	UKM Institutional Repository
collection	Online Access
language	English
description	If a Runge-Kutta method having an asymptotic error expansion in the stepsize h is symmetric then it is characterised by an h2-expansion. Since elimination of the leading error terms in succession results in an increase in the order by two at a time, a symmetric method could therefore be suitable for the construction of extrapolation methods. However, when order reduction occurs for stiff problems it needs to be suppressed before an appropriate extrapolation formula can be applied. This can be achieved by a process called symmetrization which is a composition of the symmetric method with an L-stable method known as a symmetrizer. The symmetrizer is constructed so as to preserve the h2-asymptotic error expansion. In this paper we consider symmetrization of the 2-stage Gauss and the 3-stage Lobatto IIIA methods of order 4. We show that these methods are more efficient when used with symmetrization. Extrapolation based on the symmetrized methods is therefore expected to give greater accuracy. We also show that the method with a higher stage order is more advantageous than one with a lower stage order for solving stiff problems.
format	Article
author	Robert P.K, Chan, Annie Gorgey,
spellingShingle	Robert P.K, Chan, Annie Gorgey, Order-4 symmetrized runge-kutta methods for stiff problems (Kaedah Runge-Kutta Tersimetri Peringkat-4 untuk Masalah Kaku)
author_facet	Robert P.K, Chan, Annie Gorgey,
author_sort	Robert P.K,
title	Order-4 symmetrized runge-kutta methods for stiff problems (Kaedah Runge-Kutta Tersimetri Peringkat-4 untuk Masalah Kaku)
title_short	Order-4 symmetrized runge-kutta methods for stiff problems (Kaedah Runge-Kutta Tersimetri Peringkat-4 untuk Masalah Kaku)
title_full	Order-4 symmetrized runge-kutta methods for stiff problems (Kaedah Runge-Kutta Tersimetri Peringkat-4 untuk Masalah Kaku)
title_fullStr	Order-4 symmetrized runge-kutta methods for stiff problems (Kaedah Runge-Kutta Tersimetri Peringkat-4 untuk Masalah Kaku)
title_full_unstemmed	Order-4 symmetrized runge-kutta methods for stiff problems (Kaedah Runge-Kutta Tersimetri Peringkat-4 untuk Masalah Kaku)
title_sort	order-4 symmetrized runge-kutta methods for stiff problems (kaedah runge-kutta tersimetri peringkat-4 untuk masalah kaku)
publisher	Penerbit Universiti Kebangsaan Malaysia
publishDate	2011
url	http://journalarticle.ukm.my/2890/ http://journalarticle.ukm.my/2890/ http://journalarticle.ukm.my/2890/1/jqma-7-1-05-gorgey.pdf
first_indexed	2023-09-18T19:37:15Z
last_indexed	2023-09-18T19:37:15Z
_version_	1777405353511616512

Order-4 symmetrized runge-kutta methods for stiff problems (Kaedah Runge-Kutta Tersimetri Peringkat-4 untuk Masalah Kaku)

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