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Sequential and Parallel Methods for Numerical Solutions of Delay Differential Equations

This thesis describes the development of sequential and parallel methods for solving delay differential equations. A new sequential code for the numerical solution of delay differential equations is considered. The variable order variable stepsize formulae based on the Adams-Bashforth-Moulton met...

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Main Author: Ishak, Fuziyah
Format: Thesis
Language:English
English
Published: 2009
Online Access:http://psasir.upm.edu.my/id/eprint/7556/1/ABS_----__IPM_2009_9.pdf
http://psasir.upm.edu.my/id/eprint/7556/
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spelling my.upm.eprints.75562013-05-27T07:35:35Z http://psasir.upm.edu.my/id/eprint/7556/ Sequential and Parallel Methods for Numerical Solutions of Delay Differential Equations Ishak, Fuziyah This thesis describes the development of sequential and parallel methods for solving delay differential equations. A new sequential code for the numerical solution of delay differential equations is considered. The variable order variable stepsize formulae based on the Adams-Bashforth-Moulton methods are represented in divided difference form. Derivative discontinuities are detected by local error estimate at the grid points. Large magnitude of the local error estimate indicates the presence of derivative discontinuity. Stepsize is then reduced and eventually the discontinuity point is included in the grid. The formulae representation proves to be efficient when compared with the existing method in modified divided difference form. We also consider the development of two-point block methods on sequential and parallel computers. Formulae for three two-point block methods for solving delay differential equations are derived. The implicit block methods are implemented using variable stepsize variable order technique. The formulae for two-point diagonally and triangu larly implicit block methods using predictor-corrector application are represented in divided difference form. Meanwhile, the predictor-corrector formulae for two-point fully implicit block method are calculated beforehand and stored at the beginning of the code. All of the block methods rely on the local error estimates to detect derivative discontinuities. In all of the developed methods, regions of absolute stability are presented and compared. Comparison among the developed methods indicates that all of the methods achieve the desired accuracy. Block methods are efficient when compared with the sequential non-block method as the total steps taken can be reduced. The new block methods are then used for the parallel implementation in solving large system of delay differential equations. The parallel programs using Message Passing Interface are run on Sun Fire V1280 using two processors. Numerical results indicate that parallel implementation increases the performance of the block methods. 2009 Thesis NonPeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/7556/1/ABS_----__IPM_2009_9.pdf Ishak, Fuziyah (2009) Sequential and Parallel Methods for Numerical Solutions of Delay Differential Equations. PhD thesis, Universiti Putra Malaysia. English
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
English
description This thesis describes the development of sequential and parallel methods for solving delay differential equations. A new sequential code for the numerical solution of delay differential equations is considered. The variable order variable stepsize formulae based on the Adams-Bashforth-Moulton methods are represented in divided difference form. Derivative discontinuities are detected by local error estimate at the grid points. Large magnitude of the local error estimate indicates the presence of derivative discontinuity. Stepsize is then reduced and eventually the discontinuity point is included in the grid. The formulae representation proves to be efficient when compared with the existing method in modified divided difference form. We also consider the development of two-point block methods on sequential and parallel computers. Formulae for three two-point block methods for solving delay differential equations are derived. The implicit block methods are implemented using variable stepsize variable order technique. The formulae for two-point diagonally and triangu larly implicit block methods using predictor-corrector application are represented in divided difference form. Meanwhile, the predictor-corrector formulae for two-point fully implicit block method are calculated beforehand and stored at the beginning of the code. All of the block methods rely on the local error estimates to detect derivative discontinuities. In all of the developed methods, regions of absolute stability are presented and compared. Comparison among the developed methods indicates that all of the methods achieve the desired accuracy. Block methods are efficient when compared with the sequential non-block method as the total steps taken can be reduced. The new block methods are then used for the parallel implementation in solving large system of delay differential equations. The parallel programs using Message Passing Interface are run on Sun Fire V1280 using two processors. Numerical results indicate that parallel implementation increases the performance of the block methods.
format Thesis
author Ishak, Fuziyah
spellingShingle Ishak, Fuziyah
Sequential and Parallel Methods for Numerical Solutions of Delay Differential Equations
author_facet Ishak, Fuziyah
author_sort Ishak, Fuziyah
title Sequential and Parallel Methods for Numerical Solutions of Delay Differential Equations
title_short Sequential and Parallel Methods for Numerical Solutions of Delay Differential Equations
title_full Sequential and Parallel Methods for Numerical Solutions of Delay Differential Equations
title_fullStr Sequential and Parallel Methods for Numerical Solutions of Delay Differential Equations
title_full_unstemmed Sequential and Parallel Methods for Numerical Solutions of Delay Differential Equations
title_sort sequential and parallel methods for numerical solutions of delay differential equations
publishDate 2009
url http://psasir.upm.edu.my/id/eprint/7556/1/ABS_----__IPM_2009_9.pdf
http://psasir.upm.edu.my/id/eprint/7556/
_version_ 1643823758704640000
score 13.211869

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