Parallel block methods for solving higher order ordinary differential equations directly

Numerous problems that are encountered in various branches of science and engineering involve ordinary differential equations (ODEs). Some of these problems require lengthy computation and immediate solutions. With the availability of parallel computers nowadays, the demands can be achieved. How...

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Main Author:	Omar, Zurni
Format:	Thesis
Language:	English English
Published:	1999
Subjects:	Differential equations Parallel computers Parallel processing (Electronic computers)
Online Access:	http://psasir.upm.edu.my/id/eprint/8652/1/FSAS_1999_4_IR.pdf
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id	my-upm-ir.8652
record_format	uketd_dc
spelling	my-upm-ir.86522023-12-13T02:06:19Z Parallel block methods for solving higher order ordinary differential equations directly 1999-12 Omar, Zurni Numerous problems that are encountered in various branches of science and engineering involve ordinary differential equations (ODEs). Some of these problems require lengthy computation and immediate solutions. With the availability of parallel computers nowadays, the demands can be achieved. However, most of the existing methods for solving ODEs directly, particularly of higher order, are sequential in nature. These methods approximate numerical solution at one point at a time and therefore do not fully exploit the capability of parallel computers. Hence, the development of parallel algorithms to suit these machines becomes essential. In this thesis, new explicit and implicit parallel block methods for solving a single equation of ODE directly using constant step size and back values are developed. These methods, which calculate the numerical solution at more than one point simultaneously, are parallel in nature. The programs of the methods employed are run on a shared memory Sequent Symmetry S27 parallel computer. The numerical results show that the new methods reduce the total number of steps and execution time. The accuracy of the parallel block and 1-point methods is comparable particularly when finer step sizes are used. A new parallel algorithm for solving systems of ODEs using variable step size and order is also developed. The strategies used to design this method are based on both the Direct Integration (DI) and parallel block methods. The results demonstrate the superiority of the new method in terms of the total number of steps and execution times especially with finer tolerances. In conclusion, the new methods developed can be used as viable alternatives for solving higher order ODEs directly. Differential equations Parallel computers Parallel processing (Electronic computers) 1999-12 Thesis http://psasir.upm.edu.my/id/eprint/8652/ http://psasir.upm.edu.my/id/eprint/8652/1/FSAS_1999_4_IR.pdf text en public doctoral Universiti Putra Malaysia Differential equations Parallel computers Parallel processing (Electronic computers) Faculty of Environmental Studies Suleiman, Mohamed English
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English English
advisor	Suleiman, Mohamed
topic	Differential equations Parallel computers Parallel processing (Electronic computers)
spellingShingle	Differential equations Parallel computers Parallel processing (Electronic computers) Omar, Zurni Parallel block methods for solving higher order ordinary differential equations directly
description	Numerous problems that are encountered in various branches of science and engineering involve ordinary differential equations (ODEs). Some of these problems require lengthy computation and immediate solutions. With the availability of parallel computers nowadays, the demands can be achieved. However, most of the existing methods for solving ODEs directly, particularly of higher order, are sequential in nature. These methods approximate numerical solution at one point at a time and therefore do not fully exploit the capability of parallel computers. Hence, the development of parallel algorithms to suit these machines becomes essential. In this thesis, new explicit and implicit parallel block methods for solving a single equation of ODE directly using constant step size and back values are developed. These methods, which calculate the numerical solution at more than one point simultaneously, are parallel in nature. The programs of the methods employed are run on a shared memory Sequent Symmetry S27 parallel computer. The numerical results show that the new methods reduce the total number of steps and execution time. The accuracy of the parallel block and 1-point methods is comparable particularly when finer step sizes are used. A new parallel algorithm for solving systems of ODEs using variable step size and order is also developed. The strategies used to design this method are based on both the Direct Integration (DI) and parallel block methods. The results demonstrate the superiority of the new method in terms of the total number of steps and execution times especially with finer tolerances. In conclusion, the new methods developed can be used as viable alternatives for solving higher order ODEs directly.
format	Thesis
qualification_level	Doctorate
author	Omar, Zurni
author_facet	Omar, Zurni
author_sort	Omar, Zurni
title	Parallel block methods for solving higher order ordinary differential equations directly
title_short	Parallel block methods for solving higher order ordinary differential equations directly
title_full	Parallel block methods for solving higher order ordinary differential equations directly
title_fullStr	Parallel block methods for solving higher order ordinary differential equations directly
title_full_unstemmed	Parallel block methods for solving higher order ordinary differential equations directly
title_sort	parallel block methods for solving higher order ordinary differential equations directly
granting_institution	Universiti Putra Malaysia
granting_department	Faculty of Environmental Studies
publishDate	1999
url	http://psasir.upm.edu.my/id/eprint/8652/1/FSAS_1999_4_IR.pdf
_version_	1794018767952412672

Parallel block methods for solving higher order ordinary differential equations directly

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