Variable Step Variable Order Block Backward Differentiation Method For Solving Directly Higher Order Stiff Ordinary Differential Equations

This thesis emphasises on developing Variable Step Variable Order Block Backward Differentiation Method (VSVO-BBDM) for solving directly higher-order stiff ordinary differential equations (ODEs). The scarcity of research on solving higher-order stiff ODEs directly, especially for order three and hig...

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Main Author:	Asnor, Asma Izzati
Format:	Thesis
Language:	English
Published:	2023
Subjects:	LC5800-5808 Distance education.
Online Access:	http://eprints.usm.my/60306/1/ASMA%20IZZATI%20BINTI%20ASNOR%20-%20TESIS24.pdf
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spelling	my-usm-ep.603062024-03-29T09:03:23Z Variable Step Variable Order Block Backward Differentiation Method For Solving Directly Higher Order Stiff Ordinary Differential Equations 2023-09 Asnor, Asma Izzati LC5800-5808 Distance education. This thesis emphasises on developing Variable Step Variable Order Block Backward Differentiation Method (VSVO-BBDM) for solving directly higher-order stiff ordinary differential equations (ODEs). The scarcity of research on solving higher-order stiff ODEs directly, especially for order three and higher, is evident in the existing literature. As a result, it is crucial to take up the mantle of investigating and elucidating the direct solutions for these higher-order stiff ODEs, specifically for orders three and four. This method generates a set of new solutions in a block at each integration step along the interval. The first part of the thesis discusses the computational work mth-order Variable Step Block Backward Differentiation Formula (mVS-BBDF(3)) method for direct numerical solutions of third-order stiff ODEs. These problems are directly solved without going through the reduction process to the first-order system. The mVS-BBDF(3) method is implemented in the variable step size approach. Meanwhile, the second part of this thesis comprises the computational work of the VSVO-BBDM for solving the higher-order stiff ODEs directly. The computational work of the VSVO-BBDM is carried out using a strategy of varying the step size and varying the order. The advancement of this strategy is intended to enhance the efficiency of the proposed methods to approximate the solutions effectively. Besides, a detailed discussion of the convergence and stability properties of the proposed methods is also included. 2023-09 Thesis http://eprints.usm.my/60306/ http://eprints.usm.my/60306/1/ASMA%20IZZATI%20BINTI%20ASNOR%20-%20TESIS24.pdf application/pdf en public phd doctoral Universiti Sains Malaysia Pusat Pengajian Pendidikan Jarak Jauh
institution	Universiti Sains Malaysia
collection	USM Institutional Repository
language	English
topic	LC5800-5808 Distance education.
spellingShingle	LC5800-5808 Distance education. Asnor, Asma Izzati Variable Step Variable Order Block Backward Differentiation Method For Solving Directly Higher Order Stiff Ordinary Differential Equations
description	This thesis emphasises on developing Variable Step Variable Order Block Backward Differentiation Method (VSVO-BBDM) for solving directly higher-order stiff ordinary differential equations (ODEs). The scarcity of research on solving higher-order stiff ODEs directly, especially for order three and higher, is evident in the existing literature. As a result, it is crucial to take up the mantle of investigating and elucidating the direct solutions for these higher-order stiff ODEs, specifically for orders three and four. This method generates a set of new solutions in a block at each integration step along the interval. The first part of the thesis discusses the computational work mth-order Variable Step Block Backward Differentiation Formula (mVS-BBDF(3)) method for direct numerical solutions of third-order stiff ODEs. These problems are directly solved without going through the reduction process to the first-order system. The mVS-BBDF(3) method is implemented in the variable step size approach. Meanwhile, the second part of this thesis comprises the computational work of the VSVO-BBDM for solving the higher-order stiff ODEs directly. The computational work of the VSVO-BBDM is carried out using a strategy of varying the step size and varying the order. The advancement of this strategy is intended to enhance the efficiency of the proposed methods to approximate the solutions effectively. Besides, a detailed discussion of the convergence and stability properties of the proposed methods is also included.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Asnor, Asma Izzati
author_facet	Asnor, Asma Izzati
author_sort	Asnor, Asma Izzati
title	Variable Step Variable Order Block Backward Differentiation Method For Solving Directly Higher Order Stiff Ordinary Differential Equations
title_short	Variable Step Variable Order Block Backward Differentiation Method For Solving Directly Higher Order Stiff Ordinary Differential Equations
title_full	Variable Step Variable Order Block Backward Differentiation Method For Solving Directly Higher Order Stiff Ordinary Differential Equations
title_fullStr	Variable Step Variable Order Block Backward Differentiation Method For Solving Directly Higher Order Stiff Ordinary Differential Equations
title_full_unstemmed	Variable Step Variable Order Block Backward Differentiation Method For Solving Directly Higher Order Stiff Ordinary Differential Equations
title_sort	variable step variable order block backward differentiation method for solving directly higher order stiff ordinary differential equations
granting_institution	Universiti Sains Malaysia
granting_department	Pusat Pengajian Pendidikan Jarak Jauh
publishDate	2023
url	http://eprints.usm.my/60306/1/ASMA%20IZZATI%20BINTI%20ASNOR%20-%20TESIS24.pdf
_version_	1804888909198393344

Variable Step Variable Order Block Backward Differentiation Method For Solving Directly Higher Order Stiff Ordinary Differential Equations

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