Direct Integration Block Method for Solving Higher Order Ordinary Differential Equations

In this thesis, the implicit block methods presented as in the simple form of Adams Moulton method are developed for solving higher order systems of Ordinary Differential Equations (ODEs). This method will solve the Initial Value Problems (IVPs) of second and third order ODEs using variable step siz...

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Main Author:	Azmi, Nurul Asyikin
Format:	Thesis
Language:	English English
Published:	2010
Subjects:	Differential equations
Online Access:	http://psasir.upm.edu.my/id/eprint/20377/1/IPM_2010_2019.pdf
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id	my-upm-ir.20377
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spelling	my-upm-ir.203772013-05-27T08:10:56Z Direct Integration Block Method for Solving Higher Order Ordinary Differential Equations 2010-03 Azmi, Nurul Asyikin In this thesis, the implicit block methods presented as in the simple form of Adams Moulton method are developed for solving higher order systems of Ordinary Differential Equations (ODEs). This method will solve the Initial Value Problems (IVPs) of second and third order ODEs using variable step size (VS) and variable step or variable order (VSVO) techniques. The proposed block methods will approximate the solutions at two distinct points on the x-axis simultaneously in a block. A system of higher order can also be reduced to a system of first order equations and then solved using any numerical method. This approach is very well established but it obviously will enlarge the dimension of the equations. However, the developed block method will solve the system of higher order ODEs directly without reducing it to first order. The formulae of the block method involve Lagrange’s interpolation formulae in order to compute the integration coefficients. All the coefficients will be stored in the code and there will be no computation involved for the integration coefficients. The codes were executed on UNIX operating system and the algorithms were written in C language. The numerical results showed that the performance of the developed methods gave better results in terms of total number of steps, maximum error, and total function calls compared to the existing block methods. In conclusion, the proposed implicit block methods in this thesis are appropriate for solving the second and third order ODEs. Differential equations Integration, Functional 2010-03 Thesis http://psasir.upm.edu.my/id/eprint/20377/ http://psasir.upm.edu.my/id/eprint/20377/1/IPM_2010_2019.pdf application/pdf en public masters Universiti Putra Malaysia Differential equations Integration, Functional Institute for Mathematical Research English
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English English
topic	Differential equations Differential equations
spellingShingle	Differential equations Differential equations Azmi, Nurul Asyikin Direct Integration Block Method for Solving Higher Order Ordinary Differential Equations
description	In this thesis, the implicit block methods presented as in the simple form of Adams Moulton method are developed for solving higher order systems of Ordinary Differential Equations (ODEs). This method will solve the Initial Value Problems (IVPs) of second and third order ODEs using variable step size (VS) and variable step or variable order (VSVO) techniques. The proposed block methods will approximate the solutions at two distinct points on the x-axis simultaneously in a block. A system of higher order can also be reduced to a system of first order equations and then solved using any numerical method. This approach is very well established but it obviously will enlarge the dimension of the equations. However, the developed block method will solve the system of higher order ODEs directly without reducing it to first order. The formulae of the block method involve Lagrange’s interpolation formulae in order to compute the integration coefficients. All the coefficients will be stored in the code and there will be no computation involved for the integration coefficients. The codes were executed on UNIX operating system and the algorithms were written in C language. The numerical results showed that the performance of the developed methods gave better results in terms of total number of steps, maximum error, and total function calls compared to the existing block methods. In conclusion, the proposed implicit block methods in this thesis are appropriate for solving the second and third order ODEs.
format	Thesis
qualification_level	Master's degree
author	Azmi, Nurul Asyikin
author_facet	Azmi, Nurul Asyikin
author_sort	Azmi, Nurul Asyikin
title	Direct Integration Block Method for Solving Higher Order Ordinary Differential Equations
title_short	Direct Integration Block Method for Solving Higher Order Ordinary Differential Equations
title_full	Direct Integration Block Method for Solving Higher Order Ordinary Differential Equations
title_fullStr	Direct Integration Block Method for Solving Higher Order Ordinary Differential Equations
title_full_unstemmed	Direct Integration Block Method for Solving Higher Order Ordinary Differential Equations
title_sort	direct integration block method for solving higher order ordinary differential equations
granting_institution	Universiti Putra Malaysia
granting_department	Institute for Mathematical Research
publishDate	2010
url	http://psasir.upm.edu.my/id/eprint/20377/1/IPM_2010_2019.pdf
_version_	1747811467299651584

Direct Integration Block Method for Solving Higher Order Ordinary Differential Equations

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