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A fourth-order one-step block method for solving a stiff ordinary differential equation

In this paper, we propose an A-stable one-step block method of order four for solving a stiff ordinary differential equation. This method will approximate the solutions of a stiff ordinary differential equation at three points simultaneously using a constant step size. The method is similar to the o...

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Main Authors: Mohd Zabidi, Muhammad Izzat Zakwan, Abdul Majid, Zanariah, Senu, Norazak
Format: Article
Language:English
Published: Pushpa Publishing House 2016
Online Access:http://psasir.upm.edu.my/id/eprint/56243/1/A%20fourth-order%20one-step%20block%20method%20for%20solving%20a%20stiff%20ordinary%20differential%20equation.pdf
http://psasir.upm.edu.my/id/eprint/56243/
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spelling my.upm.eprints.562432017-07-04T03:03:08Z http://psasir.upm.edu.my/id/eprint/56243/ A fourth-order one-step block method for solving a stiff ordinary differential equation Mohd Zabidi, Muhammad Izzat Zakwan Abdul Majid, Zanariah Senu, Norazak In this paper, we propose an A-stable one-step block method of order four for solving a stiff ordinary differential equation. This method will approximate the solutions of a stiff ordinary differential equation at three points simultaneously using a constant step size. The method is similar to the one-step method and it is self-starting but the implementation is based on the predictor-and-corrector formulae. Several problems have been tested in this paper to prove the efficiency and accuracy of this method. Numerical results are presented to illustrate the performance of the proposed method. The results clearly show that the proposed method is able to produce comparable and better results compared to the existing methods when solving stiff differential equations. Pushpa Publishing House 2016 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/56243/1/A%20fourth-order%20one-step%20block%20method%20for%20solving%20a%20stiff%20ordinary%20differential%20equation.pdf Mohd Zabidi, Muhammad Izzat Zakwan and Abdul Majid, Zanariah and Senu, Norazak (2016) A fourth-order one-step block method for solving a stiff ordinary differential equation. Far East Journal of Mathematical Sciences, 99 (12). pp. 1811-1831. ISSN 0972-0871
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
description In this paper, we propose an A-stable one-step block method of order four for solving a stiff ordinary differential equation. This method will approximate the solutions of a stiff ordinary differential equation at three points simultaneously using a constant step size. The method is similar to the one-step method and it is self-starting but the implementation is based on the predictor-and-corrector formulae. Several problems have been tested in this paper to prove the efficiency and accuracy of this method. Numerical results are presented to illustrate the performance of the proposed method. The results clearly show that the proposed method is able to produce comparable and better results compared to the existing methods when solving stiff differential equations.
format Article
author Mohd Zabidi, Muhammad Izzat Zakwan
Abdul Majid, Zanariah
Senu, Norazak
spellingShingle Mohd Zabidi, Muhammad Izzat Zakwan
Abdul Majid, Zanariah
Senu, Norazak
A fourth-order one-step block method for solving a stiff ordinary differential equation
author_facet Mohd Zabidi, Muhammad Izzat Zakwan
Abdul Majid, Zanariah
Senu, Norazak
author_sort Mohd Zabidi, Muhammad Izzat Zakwan
title A fourth-order one-step block method for solving a stiff ordinary differential equation
title_short A fourth-order one-step block method for solving a stiff ordinary differential equation
title_full A fourth-order one-step block method for solving a stiff ordinary differential equation
title_fullStr A fourth-order one-step block method for solving a stiff ordinary differential equation
title_full_unstemmed A fourth-order one-step block method for solving a stiff ordinary differential equation
title_sort fourth-order one-step block method for solving a stiff ordinary differential equation
publisher Pushpa Publishing House
publishDate 2016
url http://psasir.upm.edu.my/id/eprint/56243/1/A%20fourth-order%20one-step%20block%20method%20for%20solving%20a%20stiff%20ordinary%20differential%20equation.pdf
http://psasir.upm.edu.my/id/eprint/56243/
_version_ 1643836133075845120
score 13.211869

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