Extended Runge-Kutta fourth order method with polynomial interpolation technique for fuzzy population models

Uncertainty quantification plays an increasingly important role in the mathematical modeling of physical phenomena. One alternative of the mathematical modelings is provided by fuzzy sets. The main research of this thesis is the study of numerical method in solving fuzzy differential equations (FDEs...

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Main Author:	Zulkefli, Nor Atirah Izzah
Format:	Thesis
Language:	English
Published:	2019
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/99526/1/NorAtirahIzzahZulkefliPFS2019.pdf.pdf
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id	my-utm-ep.99526
record_format	uketd_dc
spelling	my-utm-ep.995262023-03-01T08:07:43Z Extended Runge-Kutta fourth order method with polynomial interpolation technique for fuzzy population models 2019 Zulkefli, Nor Atirah Izzah QA Mathematics Uncertainty quantification plays an increasingly important role in the mathematical modeling of physical phenomena. One alternative of the mathematical modelings is provided by fuzzy sets. The main research of this thesis is the study of numerical method in solving fuzzy differential equations (FDEs). In this thesis, the problem of FDEs in one-dimensional problem and two-dimensional problem were considered, namely fuzzy logistic differential equation and fuzzy predatorprey systems. The problems were solved using extended Runge-Kutta fourth order (ERK4) method. Nevertheless, due to the lacking of numerical methods available for solving polynomial type of FDEs, the ERK4 method is incorporated with polynomial interpolation technique in order to reduce the high degree of polynomials during multiplication operation. Parameter estimation provides tools for the efficient use of data in the estimation of the parameters that appears in the mathematical models. Thus, this study presents the parameter estimation using two techniques of minimization which are center difference differentiation and robust gradient minimization. Stability analysis and convergence proof of the approximation methods had been carried out. Hence, this research is carried out in order to solve these problems. The obtained numerical results prove that the ERK4 method with incorporated polynomial interpolation technique produce higher accuracy results and may become an alternative method for other uncertainty problems. 2019 Thesis http://eprints.utm.my/id/eprint/99526/ http://eprints.utm.my/id/eprint/99526/1/NorAtirahIzzahZulkefliPFS2019.pdf.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:145951 phd doctoral Universiti Teknologi Malaysia Faculty of Science - Mathematics
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Zulkefli, Nor Atirah Izzah Extended Runge-Kutta fourth order method with polynomial interpolation technique for fuzzy population models
description	Uncertainty quantification plays an increasingly important role in the mathematical modeling of physical phenomena. One alternative of the mathematical modelings is provided by fuzzy sets. The main research of this thesis is the study of numerical method in solving fuzzy differential equations (FDEs). In this thesis, the problem of FDEs in one-dimensional problem and two-dimensional problem were considered, namely fuzzy logistic differential equation and fuzzy predatorprey systems. The problems were solved using extended Runge-Kutta fourth order (ERK4) method. Nevertheless, due to the lacking of numerical methods available for solving polynomial type of FDEs, the ERK4 method is incorporated with polynomial interpolation technique in order to reduce the high degree of polynomials during multiplication operation. Parameter estimation provides tools for the efficient use of data in the estimation of the parameters that appears in the mathematical models. Thus, this study presents the parameter estimation using two techniques of minimization which are center difference differentiation and robust gradient minimization. Stability analysis and convergence proof of the approximation methods had been carried out. Hence, this research is carried out in order to solve these problems. The obtained numerical results prove that the ERK4 method with incorporated polynomial interpolation technique produce higher accuracy results and may become an alternative method for other uncertainty problems.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Zulkefli, Nor Atirah Izzah
author_facet	Zulkefli, Nor Atirah Izzah
author_sort	Zulkefli, Nor Atirah Izzah
title	Extended Runge-Kutta fourth order method with polynomial interpolation technique for fuzzy population models
title_short	Extended Runge-Kutta fourth order method with polynomial interpolation technique for fuzzy population models
title_full	Extended Runge-Kutta fourth order method with polynomial interpolation technique for fuzzy population models
title_fullStr	Extended Runge-Kutta fourth order method with polynomial interpolation technique for fuzzy population models
title_full_unstemmed	Extended Runge-Kutta fourth order method with polynomial interpolation technique for fuzzy population models
title_sort	extended runge-kutta fourth order method with polynomial interpolation technique for fuzzy population models
granting_institution	Universiti Teknologi Malaysia
granting_department	Faculty of Science - Mathematics
publishDate	2019
url	http://eprints.utm.my/id/eprint/99526/1/NorAtirahIzzahZulkefliPFS2019.pdf.pdf
_version_	1776100611768451072

Extended Runge-Kutta fourth order method with polynomial interpolation technique for fuzzy population models

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