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Block method with Hermite interpolation for numerical solution of delay differential equations

In this paper, we consider a two-point implicit block method for solving delay differential equations. For greater efficiency, the block method is implemented in variable stepsize technique. The most optimal stepsize is taken while achieving the desired accuracy. The implicit method is solved using...

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Main Authors: Ishak, Fuziyah, Abdul Majid, Zanariah, Suleiman, Mohamed
Format: Conference or Workshop Item
Language:English
Published: AIP Publishing LLC 2012
Online Access:http://psasir.upm.edu.my/id/eprint/57491/1/Block%20method%20with%20Hermite%20interpolation%20for%20numerical%20solution%20of%20delay%20differential%20equations.pdf
http://psasir.upm.edu.my/id/eprint/57491/
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spelling my.upm.eprints.574912017-09-27T11:09:04Z http://psasir.upm.edu.my/id/eprint/57491/ Block method with Hermite interpolation for numerical solution of delay differential equations Ishak, Fuziyah Abdul Majid, Zanariah Suleiman, Mohamed In this paper, we consider a two-point implicit block method for solving delay differential equations. For greater efficiency, the block method is implemented in variable stepsize technique. The most optimal stepsize is taken while achieving the desired accuracy. The implicit method is solved using predictor-corrector scheme where the corrector is iterated until convergence. Grid point formulae are derived using a predictor and a corrector of order five. The formulae produce two new values in a single integration step. Delay solutions are approximated using Hermite interpolation of order five. The advantage of using Hermite interpolation is that it requires less support points than the existing interpolation technique in order to achieve the overall accuracy. Numerical results indicate that the two-point block method with Hermite interpolation technique is efficient and reliable in solving a wide range of delay differential equations. AIP Publishing LLC 2012 Conference or Workshop Item PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/57491/1/Block%20method%20with%20Hermite%20interpolation%20for%20numerical%20solution%20of%20delay%20differential%20equations.pdf Ishak, Fuziyah and Abdul Majid, Zanariah and Suleiman, Mohamed (2012) Block method with Hermite interpolation for numerical solution of delay differential equations. In: 20th National Symposium on Mathematical Sciences (SKSM20), 18-20 Dec. 2012, Palm Garden Hotel, Putrajaya, Malaysia. (pp. 708-714). 10.1063/1.4801195
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 consider a two-point implicit block method for solving delay differential equations. For greater efficiency, the block method is implemented in variable stepsize technique. The most optimal stepsize is taken while achieving the desired accuracy. The implicit method is solved using predictor-corrector scheme where the corrector is iterated until convergence. Grid point formulae are derived using a predictor and a corrector of order five. The formulae produce two new values in a single integration step. Delay solutions are approximated using Hermite interpolation of order five. The advantage of using Hermite interpolation is that it requires less support points than the existing interpolation technique in order to achieve the overall accuracy. Numerical results indicate that the two-point block method with Hermite interpolation technique is efficient and reliable in solving a wide range of delay differential equations.
format Conference or Workshop Item
author Ishak, Fuziyah
Abdul Majid, Zanariah
Suleiman, Mohamed
spellingShingle Ishak, Fuziyah
Abdul Majid, Zanariah
Suleiman, Mohamed
Block method with Hermite interpolation for numerical solution of delay differential equations
author_facet Ishak, Fuziyah
Abdul Majid, Zanariah
Suleiman, Mohamed
author_sort Ishak, Fuziyah
title Block method with Hermite interpolation for numerical solution of delay differential equations
title_short Block method with Hermite interpolation for numerical solution of delay differential equations
title_full Block method with Hermite interpolation for numerical solution of delay differential equations
title_fullStr Block method with Hermite interpolation for numerical solution of delay differential equations
title_full_unstemmed Block method with Hermite interpolation for numerical solution of delay differential equations
title_sort block method with hermite interpolation for numerical solution of delay differential equations
publisher AIP Publishing LLC
publishDate 2012
url http://psasir.upm.edu.my/id/eprint/57491/1/Block%20method%20with%20Hermite%20interpolation%20for%20numerical%20solution%20of%20delay%20differential%20equations.pdf
http://psasir.upm.edu.my/id/eprint/57491/
_version_ 1643836503481122816
score 13.211869

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