Two-point block backward differentiation formula for solving higher order ordinary differential equations

This thesis focuses on solving higher order Ordinary Differential Equations (ODEs) directly using the Block Backward Differentiation Formula (BBDF) method. The BBDF method approximates the solution at two points concurrently. Implementation of this method is done by using equidistant stepsize on the...

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Main Author:	Zainuddin, Nooraini
Format:	Thesis
Language:	English English
Published:	2011
Subjects:	Differential equations - Numerical solutions
Online Access:	http://psasir.upm.edu.my/id/eprint/25950/1/FS%202011%2073R.pdf
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id	my-upm-ir.25950
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spelling	my-upm-ir.259502022-01-26T05:19:36Z Two-point block backward differentiation formula for solving higher order ordinary differential equations 2011-10 Zainuddin, Nooraini This thesis focuses on solving higher order Ordinary Differential Equations (ODEs) directly using the Block Backward Differentiation Formula (BBDF) method. The BBDF method approximates the solution at two points concurrently. Implementation of this method is done by using equidistant stepsize on the set of stiff problems. The first part of the thesis gives the derivation of the BBDF method for solving second order and third order stiff ODEs directly. The algorithms are written in C language and the numerical results of these methods are compared to that of reducing it to a system of first order ODEs and solves using the first order ODEs method. The subsequent part of the thesis discusses in detail the stability properties of the BBDF method which are given in the previous part. The stability properties justify the efficiency of the BBDF method as used in solving stiff problems. The illustrations of the stability region are provided. Finally, this thesis zooms into the implementation of the BBDF method using the variable order algorithm for the solution of second order stiff ODEs directly. The variable order strategies for the BBDF method is elaborated and the numerical result of the variable order BBDF method is compared with the variable order method which is available in MATLAB. In conclusion, the results show that BBDF method reduces the total number of steps and the time execution when compared to the nonblock first order ODEs method. Therefore, these new methods present significant alternatives for solving higher order ODEs directly. Differential equations - Numerical solutions 2011-10 Thesis http://psasir.upm.edu.my/id/eprint/25950/ http://psasir.upm.edu.my/id/eprint/25950/1/FS%202011%2073R.pdf application/pdf en public masters Universiti Putra Malaysia Differential equations - Numerical solutions Faculty of Science English
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English English
topic	Differential equations - Numerical solutions
spellingShingle	Differential equations - Numerical solutions Zainuddin, Nooraini Two-point block backward differentiation formula for solving higher order ordinary differential equations
description	This thesis focuses on solving higher order Ordinary Differential Equations (ODEs) directly using the Block Backward Differentiation Formula (BBDF) method. The BBDF method approximates the solution at two points concurrently. Implementation of this method is done by using equidistant stepsize on the set of stiff problems. The first part of the thesis gives the derivation of the BBDF method for solving second order and third order stiff ODEs directly. The algorithms are written in C language and the numerical results of these methods are compared to that of reducing it to a system of first order ODEs and solves using the first order ODEs method. The subsequent part of the thesis discusses in detail the stability properties of the BBDF method which are given in the previous part. The stability properties justify the efficiency of the BBDF method as used in solving stiff problems. The illustrations of the stability region are provided. Finally, this thesis zooms into the implementation of the BBDF method using the variable order algorithm for the solution of second order stiff ODEs directly. The variable order strategies for the BBDF method is elaborated and the numerical result of the variable order BBDF method is compared with the variable order method which is available in MATLAB. In conclusion, the results show that BBDF method reduces the total number of steps and the time execution when compared to the nonblock first order ODEs method. Therefore, these new methods present significant alternatives for solving higher order ODEs directly.
format	Thesis
qualification_level	Master's degree
author	Zainuddin, Nooraini
author_facet	Zainuddin, Nooraini
author_sort	Zainuddin, Nooraini
title	Two-point block backward differentiation formula for solving higher order ordinary differential equations
title_short	Two-point block backward differentiation formula for solving higher order ordinary differential equations
title_full	Two-point block backward differentiation formula for solving higher order ordinary differential equations
title_fullStr	Two-point block backward differentiation formula for solving higher order ordinary differential equations
title_full_unstemmed	Two-point block backward differentiation formula for solving higher order ordinary differential equations
title_sort	two-point block backward differentiation formula for solving higher order ordinary differential equations
granting_institution	Universiti Putra Malaysia
granting_department	Faculty of Science
publishDate	2011
url	http://psasir.upm.edu.my/id/eprint/25950/1/FS%202011%2073R.pdf
_version_	1747811536368304128

Two-point block backward differentiation formula for solving higher order ordinary differential equations

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