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Numerical solution of first order initial value problem using 7-stage tenth order Gauss-Kronrod-Lobatto IIIA method

In this paper, a new implicit Runge-Kutta method which based on a 7-point Gauss-Kronrod-Lobatto quadrature formula is developed.The resulting implicit method is a 7-stage tenth order Gauss-Kronrod-Lobatto IIIA method, or in brief as GKLM(7,10)-IIIA. GKLM(7,10)-IIIA requires seven function of evaluat...

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Main Authors: Teh, Yuan Ying, Yaacob, Nazeeruddin
Format: Conference or Workshop Item
Language:English
Published: 2013
Subjects:
QA Mathematics
Online Access:http://repo.uum.edu.my/12687/1/Teh.pdf
http://repo.uum.edu.my/12687/
http://dx.doi.org/10.1063/1.4801122
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spelling my.uum.repo.126872014-11-13T01:04:45Z http://repo.uum.edu.my/12687/ Numerical solution of first order initial value problem using 7-stage tenth order Gauss-Kronrod-Lobatto IIIA method Teh, Yuan Ying Yaacob, Nazeeruddin QA Mathematics In this paper, a new implicit Runge-Kutta method which based on a 7-point Gauss-Kronrod-Lobatto quadrature formula is developed.The resulting implicit method is a 7-stage tenth order Gauss-Kronrod-Lobatto IIIA method, or in brief as GKLM(7,10)-IIIA. GKLM(7,10)-IIIA requires seven function of evaluations at each integration step and it gives accuracy of order ten.In addition, GKLM(7,10)-IIIA has stage order seven and being A-stable. Numerical experiments compare the accuracy between GKLM(7,10)-IIIA and the classical 5-stage tenth order Gauss-Legendre method in solving some test problems. Numerical results reveal that GKLM(7,10)-IIIA is more accurate than the 5-stage tenth order Gauss-Legendre method because GKLM(7,10)-IIIA has higher stage order 2013 Conference or Workshop Item NonPeerReviewed application/pdf en http://repo.uum.edu.my/12687/1/Teh.pdf Teh, Yuan Ying and Yaacob, Nazeeruddin (2013) Numerical solution of first order initial value problem using 7-stage tenth order Gauss-Kronrod-Lobatto IIIA method. In: 20th National Symposium on Mathematical Sciences, 18–20 December 2012, Palm Garden Hotel, Putrajaya, Malaysia. (Unpublished) http://dx.doi.org/10.1063/1.4801122 doi:10.1063/1.4801122
institution Universiti Utara Malaysia
building UUM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Utara Malaysia
content_source UUM Institutionali Repository
url_provider http://repo.uum.edu.my/
language English
topic QA Mathematics
spellingShingle QA Mathematics
Teh, Yuan Ying
Yaacob, Nazeeruddin
Numerical solution of first order initial value problem using 7-stage tenth order Gauss-Kronrod-Lobatto IIIA method
description In this paper, a new implicit Runge-Kutta method which based on a 7-point Gauss-Kronrod-Lobatto quadrature formula is developed.The resulting implicit method is a 7-stage tenth order Gauss-Kronrod-Lobatto IIIA method, or in brief as GKLM(7,10)-IIIA. GKLM(7,10)-IIIA requires seven function of evaluations at each integration step and it gives accuracy of order ten.In addition, GKLM(7,10)-IIIA has stage order seven and being A-stable. Numerical experiments compare the accuracy between GKLM(7,10)-IIIA and the classical 5-stage tenth order Gauss-Legendre method in solving some test problems. Numerical results reveal that GKLM(7,10)-IIIA is more accurate than the 5-stage tenth order Gauss-Legendre method because GKLM(7,10)-IIIA has higher stage order
format Conference or Workshop Item
author Teh, Yuan Ying
Yaacob, Nazeeruddin
author_facet Teh, Yuan Ying
Yaacob, Nazeeruddin
author_sort Teh, Yuan Ying
title Numerical solution of first order initial value problem using 7-stage tenth order Gauss-Kronrod-Lobatto IIIA method
title_short Numerical solution of first order initial value problem using 7-stage tenth order Gauss-Kronrod-Lobatto IIIA method
title_full Numerical solution of first order initial value problem using 7-stage tenth order Gauss-Kronrod-Lobatto IIIA method
title_fullStr Numerical solution of first order initial value problem using 7-stage tenth order Gauss-Kronrod-Lobatto IIIA method
title_full_unstemmed Numerical solution of first order initial value problem using 7-stage tenth order Gauss-Kronrod-Lobatto IIIA method
title_sort numerical solution of first order initial value problem using 7-stage tenth order gauss-kronrod-lobatto iiia method
publishDate 2013
url http://repo.uum.edu.my/12687/1/Teh.pdf
http://repo.uum.edu.my/12687/
http://dx.doi.org/10.1063/1.4801122
_version_ 1644280974656143360
score 13.209306

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