Coupled block method for solving ordinary and delay differential equations

The idea of this thesis is to introduce two numerical methods which are known as coupled block methods for solving first order Ordinary Differential Equations (ODEs) using variable step size and order. The methods consist of two block methods which were presented as in the simple form of the Adams M...

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Main Author:	Hue, Chi San
Format:	Thesis
Language:	English English
Published:	2011
Subjects:	Differential equations - Numerical solutions Numerical analysis
Online Access:	http://psasir.upm.edu.my/id/eprint/25928/1/FS%202011%2061R.pdf
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id	my-upm-ir.25928
record_format	uketd_dc
spelling	my-upm-ir.259282022-01-26T05:12:42Z Coupled block method for solving ordinary and delay differential equations 2011-10 Hue, Chi San The idea of this thesis is to introduce two numerical methods which are known as coupled block methods for solving first order Ordinary Differential Equations (ODEs) using variable step size and order. The methods consist of two block methods which were presented as in the simple form of the Adams Moulton type. Next, the methods were implemented for solving Delay Differential Equations (DDEs) using variable step size and order. The delay term was approximated using divided difference interpolation. The stability properties of the developed block methods when applied to ODEs and DDEs were studied and their regions of stability were presented. The numerical results showed that the performance of the proposed methods are acceptable in terms of total number of steps, maximum error and execution time for solving first order ODEs and DDEs using variable step size and order. In conclusion, the methods were competitive and suitable for solving ODEs and DDEs Differential equations - Numerical solutions Numerical analysis 2011-10 Thesis http://psasir.upm.edu.my/id/eprint/25928/ http://psasir.upm.edu.my/id/eprint/25928/1/FS%202011%2061R.pdf application/pdf en public masters Universiti Putra Malaysia Differential equations - Numerical solutions Numerical analysis Faculty of Science English
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English English
topic	Differential equations - Numerical solutions Numerical analysis
spellingShingle	Differential equations - Numerical solutions Numerical analysis Hue, Chi San Coupled block method for solving ordinary and delay differential equations
description	The idea of this thesis is to introduce two numerical methods which are known as coupled block methods for solving first order Ordinary Differential Equations (ODEs) using variable step size and order. The methods consist of two block methods which were presented as in the simple form of the Adams Moulton type. Next, the methods were implemented for solving Delay Differential Equations (DDEs) using variable step size and order. The delay term was approximated using divided difference interpolation. The stability properties of the developed block methods when applied to ODEs and DDEs were studied and their regions of stability were presented. The numerical results showed that the performance of the proposed methods are acceptable in terms of total number of steps, maximum error and execution time for solving first order ODEs and DDEs using variable step size and order. In conclusion, the methods were competitive and suitable for solving ODEs and DDEs
format	Thesis
qualification_level	Master's degree
author	Hue, Chi San
author_facet	Hue, Chi San
author_sort	Hue, Chi San
title	Coupled block method for solving ordinary and delay differential equations
title_short	Coupled block method for solving ordinary and delay differential equations
title_full	Coupled block method for solving ordinary and delay differential equations
title_fullStr	Coupled block method for solving ordinary and delay differential equations
title_full_unstemmed	Coupled block method for solving ordinary and delay differential equations
title_sort	coupled block method for solving ordinary and delay differential equations
granting_institution	Universiti Putra Malaysia
granting_department	Faculty of Science
publishDate	2011
url	http://psasir.upm.edu.my/id/eprint/25928/1/FS%202011%2061R.pdf
_version_	1747811533906247680

Coupled block method for solving ordinary and delay differential equations

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