Modified exponential-rational methods for the numerical olution of first order initial value problems

Exponentially-fitted numerical methods are appealing because L-stability is guaranteed when solving initial value problems of the form Such numerical methods also yield the exact solution when solving the above-mentioned problem. Whilst rational methods have been well established in the past decades...

Full description

Bibliographic Details
Main Authors:	Teh, Yuan Ying, Zurni Omar, Kamarun Hizam Mansor
Format:	Article
Language:	English
Published:	Universiti Kebangsaan Malaysia 2014
Online Access:	http://journalarticle.ukm.my/8157/ http://journalarticle.ukm.my/8157/ http://journalarticle.ukm.my/8157/1/18_Teh_Yuan_Ying.pdf

id	ukm-8157
recordtype	eprints
spelling	ukm-81572016-12-14T06:46:23Z http://journalarticle.ukm.my/8157/ Modified exponential-rational methods for the numerical olution of first order initial value problems Teh, Yuan Ying Zurni Omar, Kamarun Hizam Mansor, Exponentially-fitted numerical methods are appealing because L-stability is guaranteed when solving initial value problems of the form Such numerical methods also yield the exact solution when solving the above-mentioned problem. Whilst rational methods have been well established in the past decades, most of them are not ‘completely’ exponentially-fitted. Recently, a class of one-step exponential-rational methods (ERMs) was discovered. Analyses showed that all ERMs are exponentially-fitted, hence implying L-stability. Several numerical experiments showed that ERMs are more accurate than existing rational methods in solving general initial value problem. However, ERMs have two weaknesses: every ERM is non-uniquely defined and may return complex values. Therefore, the purpose of this study was to modify the original ERMs so that these weaknesses will be overcome. This study discusses the generalizations of the modified ERMs and the theoretical analyses involved such as consistency, stability and convergence. Numerical experiments showed that the modified ERMs and the original ERMs are found to have comparable accuracy; hence modified ERMs are preferable to original ERMs. Universiti Kebangsaan Malaysia 2014-12 Article PeerReviewed application/pdf en http://journalarticle.ukm.my/8157/1/18_Teh_Yuan_Ying.pdf Teh, Yuan Ying and Zurni Omar, and Kamarun Hizam Mansor, (2014) Modified exponential-rational methods for the numerical olution of first order initial value problems. Sains Malaysiana, 43 (12). pp. 1951-1959. ISSN 0126-6039 http://www.ukm.my/jsm/
repository_type	Digital Repository
institution_category	Local University
institution	Universiti Kebangasaan Malaysia
building	UKM Institutional Repository
collection	Online Access
language	English
description	Exponentially-fitted numerical methods are appealing because L-stability is guaranteed when solving initial value problems of the form Such numerical methods also yield the exact solution when solving the above-mentioned problem. Whilst rational methods have been well established in the past decades, most of them are not ‘completely’ exponentially-fitted. Recently, a class of one-step exponential-rational methods (ERMs) was discovered. Analyses showed that all ERMs are exponentially-fitted, hence implying L-stability. Several numerical experiments showed that ERMs are more accurate than existing rational methods in solving general initial value problem. However, ERMs have two weaknesses: every ERM is non-uniquely defined and may return complex values. Therefore, the purpose of this study was to modify the original ERMs so that these weaknesses will be overcome. This study discusses the generalizations of the modified ERMs and the theoretical analyses involved such as consistency, stability and convergence. Numerical experiments showed that the modified ERMs and the original ERMs are found to have comparable accuracy; hence modified ERMs are preferable to original ERMs.
format	Article
author	Teh, Yuan Ying Zurni Omar, Kamarun Hizam Mansor,
spellingShingle	Teh, Yuan Ying Zurni Omar, Kamarun Hizam Mansor, Modified exponential-rational methods for the numerical olution of first order initial value problems
author_facet	Teh, Yuan Ying Zurni Omar, Kamarun Hizam Mansor,
author_sort	Teh, Yuan Ying
title	Modified exponential-rational methods for the numerical olution of first order initial value problems
title_short	Modified exponential-rational methods for the numerical olution of first order initial value problems
title_full	Modified exponential-rational methods for the numerical olution of first order initial value problems
title_fullStr	Modified exponential-rational methods for the numerical olution of first order initial value problems
title_full_unstemmed	Modified exponential-rational methods for the numerical olution of first order initial value problems
title_sort	modified exponential-rational methods for the numerical olution of first order initial value problems
publisher	Universiti Kebangsaan Malaysia
publishDate	2014
url	http://journalarticle.ukm.my/8157/ http://journalarticle.ukm.my/8157/ http://journalarticle.ukm.my/8157/1/18_Teh_Yuan_Ying.pdf
first_indexed	2023-09-18T19:51:38Z
last_indexed	2023-09-18T19:51:38Z
_version_	1777406258743083008

Modified exponential-rational methods for the numerical olution of first order initial value problems

Similar Items