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Diagonally implicit Runge-Kutta fourth order four-stage method for linear ordinary differential equations with minimized error norm

We constructed a new fourth order four-stage diagonally implicit Runge-Kutta (DIRK) method which is specially designed for the integrations of linear ordinary differential equations (LODEs). The method is obtained based on the Butcher’s error equations. In the derivation, the error norm is minimized...

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Main Authors: Che Jawias, Nur Izzati, Ismail, Fudziah, Suleiman, Mohamed, Jaafar, Azmi
Format: Article
Language:English
Published: Ibnu Sina Institute for Fundamental Science Studies, Universiti Teknologi Malaysia 2009
Online Access:http://psasir.upm.edu.my/id/eprint/14042/1/Diagonally%20implicit%20Runge-Kutta%20fourth%20order%20four-stage%20method%20for%20linear%20ordinary%20differential%20equations%20with%20minimized%20error%20norm.pdf
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id oai:psasir.upm.edu.my:14042
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spelling oai:psasir.upm.edu.my:14042 http://psasir.upm.edu.my/id/eprint/14042/ Diagonally implicit Runge-Kutta fourth order four-stage method for linear ordinary differential equations with minimized error norm Che Jawias, Nur Izzati Ismail, Fudziah Suleiman, Mohamed Jaafar, Azmi We constructed a new fourth order four-stage diagonally implicit Runge-Kutta (DIRK) method which is specially designed for the integrations of linear ordinary differential equations (LODEs). The method is obtained based on the Butcher’s error equations. In the derivation, the error norm is minimized so that the free parameters chosen are obtained from the minimized error norm. Row simplifying assumption is also used so that the number of equations for the method can be reduced and simplified. A set of test problems are used to validate the method and numerical results show that the new method is more efficient in terms of accuracy compared to the existing method. Ibnu Sina Institute for Fundamental Science Studies, Universiti Teknologi Malaysia 2009 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/14042/1/Diagonally%20implicit%20Runge-Kutta%20fourth%20order%20four-stage%20method%20for%20linear%20ordinary%20differential%20equations%20with%20minimized%20error%20norm.pdf Che Jawias, Nur Izzati and Ismail, Fudziah and Suleiman, Mohamed and Jaafar, Azmi (2009) Diagonally implicit Runge-Kutta fourth order four-stage method for linear ordinary differential equations with minimized error norm. Journal of Fundamental Sciences, 5 (1). pp. 69-78. ISSN 1823-626X https://mjfas.utm.my/index.php/mjfas/article/view/289 10.11113/mjfas.v5n1.289
institution UPM IR
collection UPM IR
language English
description We constructed a new fourth order four-stage diagonally implicit Runge-Kutta (DIRK) method which is specially designed for the integrations of linear ordinary differential equations (LODEs). The method is obtained based on the Butcher’s error equations. In the derivation, the error norm is minimized so that the free parameters chosen are obtained from the minimized error norm. Row simplifying assumption is also used so that the number of equations for the method can be reduced and simplified. A set of test problems are used to validate the method and numerical results show that the new method is more efficient in terms of accuracy compared to the existing method.
format Article
author Che Jawias, Nur Izzati
Ismail, Fudziah
Suleiman, Mohamed
Jaafar, Azmi
spellingShingle Che Jawias, Nur Izzati
Ismail, Fudziah
Suleiman, Mohamed
Jaafar, Azmi
Diagonally implicit Runge-Kutta fourth order four-stage method for linear ordinary differential equations with minimized error norm
author_facet Che Jawias, Nur Izzati
Ismail, Fudziah
Suleiman, Mohamed
Jaafar, Azmi
author_sort Che Jawias, Nur Izzati
title Diagonally implicit Runge-Kutta fourth order four-stage method for linear ordinary differential equations with minimized error norm
title_short Diagonally implicit Runge-Kutta fourth order four-stage method for linear ordinary differential equations with minimized error norm
title_full Diagonally implicit Runge-Kutta fourth order four-stage method for linear ordinary differential equations with minimized error norm
title_fullStr Diagonally implicit Runge-Kutta fourth order four-stage method for linear ordinary differential equations with minimized error norm
title_full_unstemmed Diagonally implicit Runge-Kutta fourth order four-stage method for linear ordinary differential equations with minimized error norm
title_sort diagonally implicit runge-kutta fourth order four-stage method for linear ordinary differential equations with minimized error norm
publisher Ibnu Sina Institute for Fundamental Science Studies, Universiti Teknologi Malaysia
publishDate 2009
url http://psasir.upm.edu.my/id/eprint/14042/1/Diagonally%20implicit%20Runge-Kutta%20fourth%20order%20four-stage%20method%20for%20linear%20ordinary%20differential%20equations%20with%20minimized%20error%20norm.pdf
_version_ 1819293773509689344
score 13.4562235

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