Predictor corrector block methods for solving ordinary differential equations

In this thesis, the predictor corrector block methods are developed for solving first and higher order initial value problems (lVPs) of ordinary differential equations (ODEs). These methods solve higher order ODEs problem directly without reducing to a system of first order ODEs. The derivation o...

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Main Author:	Waeleh, Nazreen
Format:	Thesis
Language:	English
Published:	2011
Subjects:	Initial value problems Differential equations - Numerical solutions
Online Access:	http://psasir.upm.edu.my/id/eprint/84973/1/FS%202011%2046%20ir.pdf
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spelling	my-upm-ir.849732021-12-31T03:03:04Z Predictor corrector block methods for solving ordinary differential equations 2011-11 Waeleh, Nazreen In this thesis, the predictor corrector block methods are developed for solving first and higher order initial value problems (lVPs) of ordinary differential equations (ODEs). These methods solve higher order ODEs problem directly without reducing to a system of first order ODEs. The derivation of these proposed block methods are based on the numerical integration method and using an interpolation approach which are similar to the Adams method. These developed block methods solve higher order ODE problems directly in a single code using variable step size strategy. In order to gain an efficient and reliable numerical approximation, these developed block methods are implemented in the predictor corrector mode using a simple iteration technique. The proposed block methods compute several numerical solutions simultaneously and the number of solutions to be computed depends on the feature of the block methods. The integration coefficients of the developed block methods formulae arc stored in the code to avoid tedious and repetitive computation. Several tested problems of ODEs are taken into account in the numerical experiments. This is to emphasize the main features of the proposed methods by comparing these direct block methods with the existing methods that solve the higher order ODEs by reducing to a system of first order ODEs. The results obtained showed that the developed block methods managed to produce acceptable results in terms of maximum error and computational time for solving higher order ODEs directly. Initial value problems Differential equations - Numerical solutions 2011-11 Thesis http://psasir.upm.edu.my/id/eprint/84973/ http://psasir.upm.edu.my/id/eprint/84973/1/FS%202011%2046%20ir.pdf text en public masters Universiti Putra Malaysia Initial value problems Differential equations - Numerical solutions Abdul Majid, Zanariah
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
advisor	Abdul Majid, Zanariah
topic	Initial value problems Differential equations - Numerical solutions
spellingShingle	Initial value problems Differential equations - Numerical solutions Waeleh, Nazreen Predictor corrector block methods for solving ordinary differential equations
description	In this thesis, the predictor corrector block methods are developed for solving first and higher order initial value problems (lVPs) of ordinary differential equations (ODEs). These methods solve higher order ODEs problem directly without reducing to a system of first order ODEs. The derivation of these proposed block methods are based on the numerical integration method and using an interpolation approach which are similar to the Adams method. These developed block methods solve higher order ODE problems directly in a single code using variable step size strategy. In order to gain an efficient and reliable numerical approximation, these developed block methods are implemented in the predictor corrector mode using a simple iteration technique. The proposed block methods compute several numerical solutions simultaneously and the number of solutions to be computed depends on the feature of the block methods. The integration coefficients of the developed block methods formulae arc stored in the code to avoid tedious and repetitive computation. Several tested problems of ODEs are taken into account in the numerical experiments. This is to emphasize the main features of the proposed methods by comparing these direct block methods with the existing methods that solve the higher order ODEs by reducing to a system of first order ODEs. The results obtained showed that the developed block methods managed to produce acceptable results in terms of maximum error and computational time for solving higher order ODEs directly.
format	Thesis
qualification_level	Master's degree
author	Waeleh, Nazreen
author_facet	Waeleh, Nazreen
author_sort	Waeleh, Nazreen
title	Predictor corrector block methods for solving ordinary differential equations
title_short	Predictor corrector block methods for solving ordinary differential equations
title_full	Predictor corrector block methods for solving ordinary differential equations
title_fullStr	Predictor corrector block methods for solving ordinary differential equations
title_full_unstemmed	Predictor corrector block methods for solving ordinary differential equations
title_sort	predictor corrector block methods for solving ordinary differential equations
granting_institution	Universiti Putra Malaysia
publishDate	2011
url	http://psasir.upm.edu.my/id/eprint/84973/1/FS%202011%2046%20ir.pdf
_version_	1747813507864199168

Predictor corrector block methods for solving ordinary differential equations

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