Finite Difference Methods For Linear Fuzzy Time Fractional Diffusion And Advection-Diffusion Equation

Fractional differential equations have attracted considerable attention in the last decade or so. This is evident from the number of publications on such equations in various scientific and engineering fields. Crisp quantities in fractional differential equations which are deemed imprecise and uncer...

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Main Author:	Zureigat, Hamzeh Husni Rasheed
Format:	Thesis
Language:	English
Published:	2019
Subjects:	QA1 Mathematics (General)
Online Access:	http://eprints.usm.my/48125/1/Hamzeh%20Husni%20Rasheed%20Zureigat%20cut.pdf
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spelling	my-usm-ep.481252021-01-19T00:41:56Z Finite Difference Methods For Linear Fuzzy Time Fractional Diffusion And Advection-Diffusion Equation 2019-08 Zureigat, Hamzeh Husni Rasheed QA1 Mathematics (General) Fractional differential equations have attracted considerable attention in the last decade or so. This is evident from the number of publications on such equations in various scientific and engineering fields. Crisp quantities in fractional differential equations which are deemed imprecise and uncertain can be replaced by fuzzy quantities to reflect imprecision and uncertainty. The fractional partial differential equation can then be expressed by fuzzy fractional partial differential equations which can give a better description for certain phenomena involving uncertainties. The analytical solution of fuzzy fractional partial differential equations is often not possible. Therefore, there is great interest in obtaining solutions via numerical methods. The finite difference method is one of the more frequently used numerical methods for solving the fractional partial differential equations due to their simplicity and universal applicability. In this thesis, the focus is the development, analysis and application of finite difference schemes of second order of accuracy and compact finite difference methods of fourth order of accuracy to solve fuzzy time fractional diffusion equation and fuzzy time fractional advection-diffusion equation. Two different fuzzy computational techniques (single and double parametric form of fuzzy number) are investigated. The Caputo formula is used to approximate the fuzzy time fractional derivative. The consistency, stability, and convergence of the finite difference methods are investigated. Numerical experiments are carried out and the results indicate the effectiveness and feasibility of the schemes that have been developed. 2019-08 Thesis http://eprints.usm.my/48125/ http://eprints.usm.my/48125/1/Hamzeh%20Husni%20Rasheed%20Zureigat%20cut.pdf application/pdf en public phd doctoral Universiti Sains Malaysia Pusat Pengajian Sains Matematik
institution	Universiti Sains Malaysia
collection	USM Institutional Repository
language	English
topic	QA1 Mathematics (General)
spellingShingle	QA1 Mathematics (General) Zureigat, Hamzeh Husni Rasheed Finite Difference Methods For Linear Fuzzy Time Fractional Diffusion And Advection-Diffusion Equation
description	Fractional differential equations have attracted considerable attention in the last decade or so. This is evident from the number of publications on such equations in various scientific and engineering fields. Crisp quantities in fractional differential equations which are deemed imprecise and uncertain can be replaced by fuzzy quantities to reflect imprecision and uncertainty. The fractional partial differential equation can then be expressed by fuzzy fractional partial differential equations which can give a better description for certain phenomena involving uncertainties. The analytical solution of fuzzy fractional partial differential equations is often not possible. Therefore, there is great interest in obtaining solutions via numerical methods. The finite difference method is one of the more frequently used numerical methods for solving the fractional partial differential equations due to their simplicity and universal applicability. In this thesis, the focus is the development, analysis and application of finite difference schemes of second order of accuracy and compact finite difference methods of fourth order of accuracy to solve fuzzy time fractional diffusion equation and fuzzy time fractional advection-diffusion equation. Two different fuzzy computational techniques (single and double parametric form of fuzzy number) are investigated. The Caputo formula is used to approximate the fuzzy time fractional derivative. The consistency, stability, and convergence of the finite difference methods are investigated. Numerical experiments are carried out and the results indicate the effectiveness and feasibility of the schemes that have been developed.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Zureigat, Hamzeh Husni Rasheed
author_facet	Zureigat, Hamzeh Husni Rasheed
author_sort	Zureigat, Hamzeh Husni Rasheed
title	Finite Difference Methods For Linear Fuzzy Time Fractional Diffusion And Advection-Diffusion Equation
title_short	Finite Difference Methods For Linear Fuzzy Time Fractional Diffusion And Advection-Diffusion Equation
title_full	Finite Difference Methods For Linear Fuzzy Time Fractional Diffusion And Advection-Diffusion Equation
title_fullStr	Finite Difference Methods For Linear Fuzzy Time Fractional Diffusion And Advection-Diffusion Equation
title_full_unstemmed	Finite Difference Methods For Linear Fuzzy Time Fractional Diffusion And Advection-Diffusion Equation
title_sort	finite difference methods for linear fuzzy time fractional diffusion and advection-diffusion equation
granting_institution	Universiti Sains Malaysia
granting_department	Pusat Pengajian Sains Matematik
publishDate	2019
url	http://eprints.usm.my/48125/1/Hamzeh%20Husni%20Rasheed%20Zureigat%20cut.pdf
_version_	1747821884438740992

Finite Difference Methods For Linear Fuzzy Time Fractional Diffusion And Advection-Diffusion Equation

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