A class of hybrid multistep block methods with a–stability for the numerical solution of stiff ordinary differential equations

Recently, block backward differentiation formulas (BBDFs) are used successfully for solving stiff differential equations. In this article, a class of hybrid block backward differentiation formulas (HBBDFs) methods that possessed A –stability are constructed by reformulating the BBDFs for the numeric...

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Main Authors: Ibrahim, Zarina Bibi, Mohd Nasarudin, Amiratul Ashikin
Format: Article
Language:English
Published: Multidisciplinary Digital Publishing Institute 2020
Online Access:http://psasir.upm.edu.my/id/eprint/87576/
http://psasir.upm.edu.my/id/eprint/87576/1/ABSTRACT.pdf
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author Ibrahim, Zarina Bibi
Mohd Nasarudin, Amiratul Ashikin
author_facet Ibrahim, Zarina Bibi
Mohd Nasarudin, Amiratul Ashikin
author_sort Ibrahim, Zarina Bibi
building UPM Institutional Repository
collection Online Access
description Recently, block backward differentiation formulas (BBDFs) are used successfully for solving stiff differential equations. In this article, a class of hybrid block backward differentiation formulas (HBBDFs) methods that possessed A –stability are constructed by reformulating the BBDFs for the numerical solution of stiff ordinary differential equations (ODEs). The stability and convergence of the new method are investigated. The methods are found to be zero-stable and consistent, hence the method is convergent. Comparisons between the proposed method with exact solutions and existing methods of similar type show that the new extension of the BBDFs improved the stability with acceptable degree of accuracy.
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spelling upm-875762022-07-06T08:35:19Z http://psasir.upm.edu.my/id/eprint/87576/ A class of hybrid multistep block methods with a–stability for the numerical solution of stiff ordinary differential equations Ibrahim, Zarina Bibi Mohd Nasarudin, Amiratul Ashikin Recently, block backward differentiation formulas (BBDFs) are used successfully for solving stiff differential equations. In this article, a class of hybrid block backward differentiation formulas (HBBDFs) methods that possessed A –stability are constructed by reformulating the BBDFs for the numerical solution of stiff ordinary differential equations (ODEs). The stability and convergence of the new method are investigated. The methods are found to be zero-stable and consistent, hence the method is convergent. Comparisons between the proposed method with exact solutions and existing methods of similar type show that the new extension of the BBDFs improved the stability with acceptable degree of accuracy. Multidisciplinary Digital Publishing Institute 2020 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/87576/1/ABSTRACT.pdf Ibrahim, Zarina Bibi and Mohd Nasarudin, Amiratul Ashikin (2020) A class of hybrid multistep block methods with a–stability for the numerical solution of stiff ordinary differential equations. Mathematics, 8 (6). pp. 1-19. ISSN 2227-7390 https://www.mdpi.com/2227-7390/8/6/914 10.3390/math8060914
spellingShingle Ibrahim, Zarina Bibi
Mohd Nasarudin, Amiratul Ashikin
A class of hybrid multistep block methods with a–stability for the numerical solution of stiff ordinary differential equations
title A class of hybrid multistep block methods with a–stability for the numerical solution of stiff ordinary differential equations
title_full A class of hybrid multistep block methods with a–stability for the numerical solution of stiff ordinary differential equations
title_fullStr A class of hybrid multistep block methods with a–stability for the numerical solution of stiff ordinary differential equations
title_full_unstemmed A class of hybrid multistep block methods with a–stability for the numerical solution of stiff ordinary differential equations
title_short A class of hybrid multistep block methods with a–stability for the numerical solution of stiff ordinary differential equations
title_sort class of hybrid multistep block methods with a–stability for the numerical solution of stiff ordinary differential equations
url http://psasir.upm.edu.my/id/eprint/87576/
http://psasir.upm.edu.my/id/eprint/87576/
http://psasir.upm.edu.my/id/eprint/87576/
http://psasir.upm.edu.my/id/eprint/87576/1/ABSTRACT.pdf