Interval wise block partitioning using three points for solving stiff systems ordinary differential equations / Mahfuzah Mahayadin

Partitioning is a strategy for solving stiff systems of ordinary differential equations (ODEs) problems. There are two types of partitioning; intervalwise and componentwise partitioning. This thesis is focused only on intervalwise block partitioning (IBP) which the system of equations will initially...

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Main Author:	Mahayadin, Mahfuzah
Format:	Thesis
Language:	English
Published:	2014
Subjects:	Equations Analytic mechanics
Online Access:	https://ir.uitm.edu.my/id/eprint/48517/1/48517.pdf
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spelling	my-uitm-ir.485172023-01-19T02:53:53Z Interval wise block partitioning using three points for solving stiff systems ordinary differential equations / Mahfuzah Mahayadin 2014 Mahayadin, Mahfuzah Equations Analytic mechanics Partitioning is a strategy for solving stiff systems of ordinary differential equations (ODEs) problems. There are two types of partitioning; intervalwise and componentwise partitioning. This thesis is focused only on intervalwise block partitioning (IBP) which the system of equations will initially be treated as non-stiff subsystem and will be solved using Adams block method. Once an equation is identified as stiff, the whole system will be treated as stiff and will be solved using block Backward Differentiation Formulae (BBDF). This process will continue until the integration interval is completed. In addition, variable step size BBDF (VSBBDF) method using three points is derived in order to solve first order stiff ODEs. The partitioning strategy involved is based on Adams method formulae and VSBBDF formulae. A single code is developed based on variable step size IBP. The code is implemented using Microsoft Visual C++ 6.0 XP Version and compared with odel5s and ode23s which are run in MATLAB 7.8. The numerical results have shown that the partitioning strategy has performed well in term of computational time compared to VSBBDF and MATLAB ode solvers, odel5s and ode23s. It shows that the partitioning strategy can be an alternative method to solve first order stiff ODEs. 2014 Thesis https://ir.uitm.edu.my/id/eprint/48517/ https://ir.uitm.edu.my/id/eprint/48517/1/48517.pdf text en public masters Universiti Teknologi MARA (UiTM) Faculty of Computer and Mathematical Sciences Othman, Khairil Iskandar
institution	Universiti Teknologi MARA
collection	UiTM Institutional Repository
language	English
advisor	Othman, Khairil Iskandar
topic	Equations Analytic mechanics
spellingShingle	Equations Analytic mechanics Mahayadin, Mahfuzah Interval wise block partitioning using three points for solving stiff systems ordinary differential equations / Mahfuzah Mahayadin
description	Partitioning is a strategy for solving stiff systems of ordinary differential equations (ODEs) problems. There are two types of partitioning; intervalwise and componentwise partitioning. This thesis is focused only on intervalwise block partitioning (IBP) which the system of equations will initially be treated as non-stiff subsystem and will be solved using Adams block method. Once an equation is identified as stiff, the whole system will be treated as stiff and will be solved using block Backward Differentiation Formulae (BBDF). This process will continue until the integration interval is completed. In addition, variable step size BBDF (VSBBDF) method using three points is derived in order to solve first order stiff ODEs. The partitioning strategy involved is based on Adams method formulae and VSBBDF formulae. A single code is developed based on variable step size IBP. The code is implemented using Microsoft Visual C++ 6.0 XP Version and compared with odel5s and ode23s which are run in MATLAB 7.8. The numerical results have shown that the partitioning strategy has performed well in term of computational time compared to VSBBDF and MATLAB ode solvers, odel5s and ode23s. It shows that the partitioning strategy can be an alternative method to solve first order stiff ODEs.
format	Thesis
qualification_level	Master's degree
author	Mahayadin, Mahfuzah
author_facet	Mahayadin, Mahfuzah
author_sort	Mahayadin, Mahfuzah
title	Interval wise block partitioning using three points for solving stiff systems ordinary differential equations / Mahfuzah Mahayadin
title_short	Interval wise block partitioning using three points for solving stiff systems ordinary differential equations / Mahfuzah Mahayadin
title_full	Interval wise block partitioning using three points for solving stiff systems ordinary differential equations / Mahfuzah Mahayadin
title_fullStr	Interval wise block partitioning using three points for solving stiff systems ordinary differential equations / Mahfuzah Mahayadin
title_full_unstemmed	Interval wise block partitioning using three points for solving stiff systems ordinary differential equations / Mahfuzah Mahayadin
title_sort	interval wise block partitioning using three points for solving stiff systems ordinary differential equations / mahfuzah mahayadin
granting_institution	Universiti Teknologi MARA (UiTM)
granting_department	Faculty of Computer and Mathematical Sciences
publishDate	2014
url	https://ir.uitm.edu.my/id/eprint/48517/1/48517.pdf
_version_	1783734787771465728

Interval wise block partitioning using three points for solving stiff systems ordinary differential equations / Mahfuzah Mahayadin

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