Hybrid runge-kutta method for solving linear fuzzy delay differential equations with unknown state-delays

In this research, a new method to solve the Fuzzy Delay Differential Equations (FDDEs) with unknown state-delays constrained optimization problem is introduced. This method is based on the coupling of second and third orders Runge- Kutta (RK) method called hybrid RK method. The main goal of this the...

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Main Author:	Lim, Rui Sih
Format:	Thesis
Language:	English
Published:	2020
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/101899/1/LimRuiSihPFS2020.pdf.pdf
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id	my-utm-ep.101899
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spelling	my-utm-ep.1018992023-07-22T03:20:48Z Hybrid runge-kutta method for solving linear fuzzy delay differential equations with unknown state-delays 2020 Lim, Rui Sih QA Mathematics In this research, a new method to solve the Fuzzy Delay Differential Equations (FDDEs) with unknown state-delays constrained optimization problem is introduced. This method is based on the coupling of second and third orders Runge- Kutta (RK) method called hybrid RK method. The main goal of this thesis is to identify the unknown state-delays using experimental data. RK methods are chosen because they are well-established and can be easily modified to overcome the discontinuities which occur in Delay Differential Equations (DDEs) especially outside uniform nodes with delay step-size. Numerical results of FDDEs from the hybrid RK methods are compared with exact solutions derived from stepwise approach using Maple software. The relative errors are calculated for the purpose of accuracy checking on these numerical schemes. In this study, a dynamic optimization problem in which the state-delays are decision variables is also imposed; with its formulated cost function. The gradient of the cost function is computed by solving auxiliary FDDEs. By exploiting the results, the state-delay identification problem can be solved efficiently and accurately using a gradient-based optimization method. In addition, a C program has been developed based on hybrid RK methods for solving these problems. Consequently, the results show that the new hybrid scheme is an efficient numerical technique in solving all the problems above with acceptable errors. 2020 Thesis http://eprints.utm.my/id/eprint/101899/ http://eprints.utm.my/id/eprint/101899/1/LimRuiSihPFS2020.pdf.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:145997 phd doctoral Universiti Teknologi Malaysia Faculty of Science
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Lim, Rui Sih Hybrid runge-kutta method for solving linear fuzzy delay differential equations with unknown state-delays
description	In this research, a new method to solve the Fuzzy Delay Differential Equations (FDDEs) with unknown state-delays constrained optimization problem is introduced. This method is based on the coupling of second and third orders Runge- Kutta (RK) method called hybrid RK method. The main goal of this thesis is to identify the unknown state-delays using experimental data. RK methods are chosen because they are well-established and can be easily modified to overcome the discontinuities which occur in Delay Differential Equations (DDEs) especially outside uniform nodes with delay step-size. Numerical results of FDDEs from the hybrid RK methods are compared with exact solutions derived from stepwise approach using Maple software. The relative errors are calculated for the purpose of accuracy checking on these numerical schemes. In this study, a dynamic optimization problem in which the state-delays are decision variables is also imposed; with its formulated cost function. The gradient of the cost function is computed by solving auxiliary FDDEs. By exploiting the results, the state-delay identification problem can be solved efficiently and accurately using a gradient-based optimization method. In addition, a C program has been developed based on hybrid RK methods for solving these problems. Consequently, the results show that the new hybrid scheme is an efficient numerical technique in solving all the problems above with acceptable errors.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Lim, Rui Sih
author_facet	Lim, Rui Sih
author_sort	Lim, Rui Sih
title	Hybrid runge-kutta method for solving linear fuzzy delay differential equations with unknown state-delays
title_short	Hybrid runge-kutta method for solving linear fuzzy delay differential equations with unknown state-delays
title_full	Hybrid runge-kutta method for solving linear fuzzy delay differential equations with unknown state-delays
title_fullStr	Hybrid runge-kutta method for solving linear fuzzy delay differential equations with unknown state-delays
title_full_unstemmed	Hybrid runge-kutta method for solving linear fuzzy delay differential equations with unknown state-delays
title_sort	hybrid runge-kutta method for solving linear fuzzy delay differential equations with unknown state-delays
granting_institution	Universiti Teknologi Malaysia
granting_department	Faculty of Science
publishDate	2020
url	http://eprints.utm.my/id/eprint/101899/1/LimRuiSihPFS2020.pdf.pdf
_version_	1776100798367793152

Hybrid runge-kutta method for solving linear fuzzy delay differential equations with unknown state-delays

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