Numerical solution of fractional partial differential equations by spectral methods

Numerical solution of fractional partial differential equations by spectral methods

Fractional partial differential equations (FPDEs) have become essential tool for the modeling of physical models by using spectral methods. In the last few decades, spectral methods have been developed for the solution of time and space dimensional FPDEs. There are different types of spectral method...

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Main Author: Kanwal, Afshan
Format: Thesis
Language:English
English
English
Published: 2019
Subjects:
QA Mathematics
Online Access:http://eprints.uthm.edu.my/44/1/24p%20AFSHAN%20KANWAL.pdf
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spelling my-uthm-ep.442021-06-22T03:21:33Z Numerical solution of fractional partial differential equations by spectral methods 2019-09 Kanwal, Afshan QA Mathematics Fractional partial differential equations (FPDEs) have become essential tool for the modeling of physical models by using spectral methods. In the last few decades, spectral methods have been developed for the solution of time and space dimensional FPDEs. There are different types of spectral methods such as collocation methods, Tau methods and Galerkin methods. This research work focuses on the collocation and Tau methods to propose an efficient operational matrix methods via Genocchi polynomials and Legendre polynomials for the solution of two and three dimensional FPDEs. Moreover, in this study, Genocchi wavelet-like basis method and Genocchi polynomials based Ritz- Galerkin method have been derived to deal with FPDEs and variable- order FPDEs. The reason behind using the Genocchi polynomials is that, it helps to generate functional expansions with less degree and small coefficients values to derive the operational matrix of derivative with less computational complexity as compared to Chebyshev and Legendre Polynomials. The results have been compared with the existing methods such as Chebyshev wavelets method, Legendre wavelets method, Adomian decomposition method, Variational iteration method, Finite difference method and Finite element method. The numerical results have revealed that the proposed methods have provided the better results as compared to existing methods due to minimum computational complexity of derived operational matrices via Genocchi polynomials. Additionally, the significance of the proposed methods has been verified by finding the error bound, which shows that the proposed methods have provided better approximation values for under consideration FPDEs. 2019-09 Thesis http://eprints.uthm.edu.my/44/ http://eprints.uthm.edu.my/44/1/24p%20AFSHAN%20KANWAL.pdf text en public http://eprints.uthm.edu.my/44/2/AFSHAN%20KANWAL%20COPYRIGHT%20DECLARATION.pdf text en staffonly http://eprints.uthm.edu.my/44/3/AFSHAN%20KANWAL%20WATERMARK.pdf text en validuser phd doctoral Universiti Tun Hussein Onn Malaysia Fakulti Sains Gunaan dan Teknolgi
institution Universiti Tun Hussein Onn Malaysia
collection UTHM Institutional Repository
language English
English
English
topic QA Mathematics
spellingShingle QA Mathematics
Kanwal, Afshan
Numerical solution of fractional partial differential equations by spectral methods
description Fractional partial differential equations (FPDEs) have become essential tool for the modeling of physical models by using spectral methods. In the last few decades, spectral methods have been developed for the solution of time and space dimensional FPDEs. There are different types of spectral methods such as collocation methods, Tau methods and Galerkin methods. This research work focuses on the collocation and Tau methods to propose an efficient operational matrix methods via Genocchi polynomials and Legendre polynomials for the solution of two and three dimensional FPDEs. Moreover, in this study, Genocchi wavelet-like basis method and Genocchi polynomials based Ritz- Galerkin method have been derived to deal with FPDEs and variable- order FPDEs. The reason behind using the Genocchi polynomials is that, it helps to generate functional expansions with less degree and small coefficients values to derive the operational matrix of derivative with less computational complexity as compared to Chebyshev and Legendre Polynomials. The results have been compared with the existing methods such as Chebyshev wavelets method, Legendre wavelets method, Adomian decomposition method, Variational iteration method, Finite difference method and Finite element method. The numerical results have revealed that the proposed methods have provided the better results as compared to existing methods due to minimum computational complexity of derived operational matrices via Genocchi polynomials. Additionally, the significance of the proposed methods has been verified by finding the error bound, which shows that the proposed methods have provided better approximation values for under consideration FPDEs.
format Thesis
qualification_name Doctor of Philosophy (PhD.)
qualification_level Doctorate
author Kanwal, Afshan
author_facet Kanwal, Afshan
author_sort Kanwal, Afshan
title Numerical solution of fractional partial differential equations by spectral methods
title_short Numerical solution of fractional partial differential equations by spectral methods
title_full Numerical solution of fractional partial differential equations by spectral methods
title_fullStr Numerical solution of fractional partial differential equations by spectral methods
title_full_unstemmed Numerical solution of fractional partial differential equations by spectral methods
title_sort numerical solution of fractional partial differential equations by spectral methods
granting_institution Universiti Tun Hussein Onn Malaysia
granting_department Fakulti Sains Gunaan dan Teknolgi
publishDate 2019
url http://eprints.uthm.edu.my/44/1/24p%20AFSHAN%20KANWAL.pdf
http://eprints.uthm.edu.my/44/2/AFSHAN%20KANWAL%20COPYRIGHT%20DECLARATION.pdf
http://eprints.uthm.edu.my/44/3/AFSHAN%20KANWAL%20WATERMARK.pdf
_version_ 1747830515014041600

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