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Two point block method in variable stepsize technique for solving delay differential equations

Delay differential equations play an important role in modeling many real life phenomena. The application areas of delay differential equations include the fields of engineering, biology and economy. In this paper, we describe the development and the stability analysis of a two-point implicit block...

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Main Authors: Ishak, Fuziyah, Abdul Majid, Zanariah, Suleiman, Mohamed
Format: Article
Language:English
Published: David Publishing Company 2010
Online Access:http://psasir.upm.edu.my/id/eprint/17500/1/Two-Point%20Block%20Method%20in%20Variable%20Stepsize%20Technique.pdf
http://psasir.upm.edu.my/id/eprint/17500/
http://www.davidpublishing.com/show.html?17199
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spelling my.upm.eprints.175002015-09-01T01:14:57Z http://psasir.upm.edu.my/id/eprint/17500/ Two point block method in variable stepsize technique for solving delay differential equations Ishak, Fuziyah Abdul Majid, Zanariah Suleiman, Mohamed Delay differential equations play an important role in modeling many real life phenomena. The application areas of delay differential equations include the fields of engineering, biology and economy. In this paper, we describe the development and the stability analysis of a two-point implicit block method for solving delay differential equations. The method produces two new values at a single step of integration. The implicit formulae are derived by using a predictor of order four and a corrector of order five. The method is implemented by using the variable stepsize technique and the predictor-corrector scheme is iterated until convergence. In variable stepsize approach, the integration coefficients need to be recalculated whenever a step size changes. These tedious calculations are avoided by deriving the formulae beforehand and storing the coefficients at the start of the code. In preserving the order of the method, the number of interpolation points for approximating delay solution is one higher than the order of the method at grid point. The numerical results suggest that the two-point implicit block method provides an efficient, reliable and accurate way of solving a wide range of delay differential equations. We also consider the stability analysis of the two-point block method by numerically examining the stability polynomials of the method. P-and Q-stability regions for the variable stepsize formulae are illustrated. David Publishing Company 2010-12 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/17500/1/Two-Point%20Block%20Method%20in%20Variable%20Stepsize%20Technique.pdf Ishak, Fuziyah and Abdul Majid, Zanariah and Suleiman, Mohamed (2010) Two point block method in variable stepsize technique for solving delay differential equations. Journal of Materials Science and Engineering, 4 (12). pp. 86-90. ISSN 1934-8959 http://www.davidpublishing.com/show.html?17199
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 Delay differential equations play an important role in modeling many real life phenomena. The application areas of delay differential equations include the fields of engineering, biology and economy. In this paper, we describe the development and the stability analysis of a two-point implicit block method for solving delay differential equations. The method produces two new values at a single step of integration. The implicit formulae are derived by using a predictor of order four and a corrector of order five. The method is implemented by using the variable stepsize technique and the predictor-corrector scheme is iterated until convergence. In variable stepsize approach, the integration coefficients need to be recalculated whenever a step size changes. These tedious calculations are avoided by deriving the formulae beforehand and storing the coefficients at the start of the code. In preserving the order of the method, the number of interpolation points for approximating delay solution is one higher than the order of the method at grid point. The numerical results suggest that the two-point implicit block method provides an efficient, reliable and accurate way of solving a wide range of delay differential equations. We also consider the stability analysis of the two-point block method by numerically examining the stability polynomials of the method. P-and Q-stability regions for the variable stepsize formulae are illustrated.
format Article
author Ishak, Fuziyah
Abdul Majid, Zanariah
Suleiman, Mohamed
spellingShingle Ishak, Fuziyah
Abdul Majid, Zanariah
Suleiman, Mohamed
Two point block method in variable stepsize technique for solving delay differential equations
author_facet Ishak, Fuziyah
Abdul Majid, Zanariah
Suleiman, Mohamed
author_sort Ishak, Fuziyah
title Two point block method in variable stepsize technique for solving delay differential equations
title_short Two point block method in variable stepsize technique for solving delay differential equations
title_full Two point block method in variable stepsize technique for solving delay differential equations
title_fullStr Two point block method in variable stepsize technique for solving delay differential equations
title_full_unstemmed Two point block method in variable stepsize technique for solving delay differential equations
title_sort two point block method in variable stepsize technique for solving delay differential equations
publisher David Publishing Company
publishDate 2010
url http://psasir.upm.edu.my/id/eprint/17500/1/Two-Point%20Block%20Method%20in%20Variable%20Stepsize%20Technique.pdf
http://psasir.upm.edu.my/id/eprint/17500/
http://www.davidpublishing.com/show.html?17199
_version_ 1643826536235663360
score 13.211869

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