New forms of Bézier control points and b-spline methods for solving fuzzy ordinary differential equations

Fuzzy ordinary differential equations (FODEs) are widely used to model many problems in science and engineering and have been studied by many researchers. Specific problems require the solutions of FODEs, which satisfy fuzzy initial conditions for fuzzy initial value problems (FIVPs) and fuzzy bound...

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Main Author:	Aljabbari, Sardar Gul Amen
Format:	Thesis
Language:	eng eng eng
Published:	2023
Subjects:	QA76.76 Fuzzy System.
Online Access:	https://etd.uum.edu.my/10691/1/permission%20to%20deposit-not%20allow-s903023.pdf https://etd.uum.edu.my/10691/2/s903023_01.pdf https://etd.uum.edu.my/10691/3/s903023_02.pdf
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id	my-uum-etd.10691
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spelling	my-uum-etd.106912023-10-16T06:28:39Z New forms of Bézier control points and b-spline methods for solving fuzzy ordinary differential equations 2023 Aljabbari, Sardar Gul Amen Jameel, Ali Fareed Yaakob, Abdul Malek Awang Had Salleh Graduate School of Arts & Sciences Awang Had Salleh Graduate School of Art & Sciences QA76.76 Fuzzy System. Fuzzy ordinary differential equations (FODEs) are widely used to model many problems in science and engineering and have been studied by many researchers. Specific problems require the solutions of FODEs, which satisfy fuzzy initial conditions for fuzzy initial value problems (FIVPs) and fuzzy boundary conditions for fuzzy boundary value problems (FBVPs). Such problems can be found in physics, engineering, population models, nuclear reactor dynamics, medical problems, neural networks, and control theory. However, most FIVPs and FBVPs cannot be solved exactly. Furthermore, exact solutions may also be too difficult to obtain for some problems. Therefore, numerical and approximate methods are necessary to be considered for the solutions. In the last two decades, the development of approximate methods to solve these equations has been an important area of research. Therefore, this thesis needs to modify and formulate new, efficient, and more accurate methods, which are the main focus. This thesis proposes new approximate methods based on fuzzy set theory properties with the Bézier control points method (BCPM) and B-Spline method (BSM) to solve first- and nth-order linear and nonlinear FODEs involving FIVPs and FBVPs. We also conduct the error and convergence analysis of the method. We modified and formulated these methods to solve linear and nonlinear nth-order FIVPs and FBVPs directly without reducing them into a first-order system, as done by most other researchers. Some test examples are given to illustrate the proposed methods' feasibility and accuracy. In general, the numerical results indicate that the proposed BCPM and BSM provide better accuracy than the existing approximate-analytical methods. Hence, the BCPM and BSM are viable alternative methods for solving FIVPs and FBVPs. 2023 Thesis https://etd.uum.edu.my/10691/ https://etd.uum.edu.my/10691/1/permission%20to%20deposit-not%20allow-s903023.pdf text eng staffonly https://etd.uum.edu.my/10691/2/s903023_01.pdf text eng staffonly https://etd.uum.edu.my/10691/3/s903023_02.pdf text eng staffonly other doctoral Universiti Utara Malaysia
institution	Universiti Utara Malaysia
collection	UUM ETD
language	eng eng eng
advisor	Jameel, Ali Fareed Yaakob, Abdul Malek
topic	QA76.76 Fuzzy System.
spellingShingle	QA76.76 Fuzzy System. Aljabbari, Sardar Gul Amen New forms of Bézier control points and b-spline methods for solving fuzzy ordinary differential equations
description	Fuzzy ordinary differential equations (FODEs) are widely used to model many problems in science and engineering and have been studied by many researchers. Specific problems require the solutions of FODEs, which satisfy fuzzy initial conditions for fuzzy initial value problems (FIVPs) and fuzzy boundary conditions for fuzzy boundary value problems (FBVPs). Such problems can be found in physics, engineering, population models, nuclear reactor dynamics, medical problems, neural networks, and control theory. However, most FIVPs and FBVPs cannot be solved exactly. Furthermore, exact solutions may also be too difficult to obtain for some problems. Therefore, numerical and approximate methods are necessary to be considered for the solutions. In the last two decades, the development of approximate methods to solve these equations has been an important area of research. Therefore, this thesis needs to modify and formulate new, efficient, and more accurate methods, which are the main focus. This thesis proposes new approximate methods based on fuzzy set theory properties with the Bézier control points method (BCPM) and B-Spline method (BSM) to solve first- and nth-order linear and nonlinear FODEs involving FIVPs and FBVPs. We also conduct the error and convergence analysis of the method. We modified and formulated these methods to solve linear and nonlinear nth-order FIVPs and FBVPs directly without reducing them into a first-order system, as done by most other researchers. Some test examples are given to illustrate the proposed methods' feasibility and accuracy. In general, the numerical results indicate that the proposed BCPM and BSM provide better accuracy than the existing approximate-analytical methods. Hence, the BCPM and BSM are viable alternative methods for solving FIVPs and FBVPs.
format	Thesis
qualification_name	other
qualification_level	Doctorate
author	Aljabbari, Sardar Gul Amen
author_facet	Aljabbari, Sardar Gul Amen
author_sort	Aljabbari, Sardar Gul Amen
title	New forms of Bézier control points and b-spline methods for solving fuzzy ordinary differential equations
title_short	New forms of Bézier control points and b-spline methods for solving fuzzy ordinary differential equations
title_full	New forms of Bézier control points and b-spline methods for solving fuzzy ordinary differential equations
title_fullStr	New forms of Bézier control points and b-spline methods for solving fuzzy ordinary differential equations
title_full_unstemmed	New forms of Bézier control points and b-spline methods for solving fuzzy ordinary differential equations
title_sort	new forms of bézier control points and b-spline methods for solving fuzzy ordinary differential equations
granting_institution	Universiti Utara Malaysia
granting_department	Awang Had Salleh Graduate School of Arts & Sciences
publishDate	2023
url	https://etd.uum.edu.my/10691/1/permission%20to%20deposit-not%20allow-s903023.pdf https://etd.uum.edu.my/10691/2/s903023_01.pdf https://etd.uum.edu.my/10691/3/s903023_02.pdf
_version_	1783729404844703744

New forms of Bézier control points and b-spline methods for solving fuzzy ordinary differential equations

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