B-Splines Based Finite Difference Schemes For Fractional Partial Differential Equations

Fractional partial differential equations (FPDEs) are considered to be the extended formulation of classical partial differential equations (PDEs). Several physical models in certain fields of sciences and engineering are more appropriately formulated in the form of FPDEs. FPDEs in general, do not...

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Main Author:	Akram, Tayyaba
Format:	Thesis
Language:	English
Published:	2020
Subjects:	QA1-939 Mathematics
Online Access:	http://eprints.usm.my/55571/1/Pages%20from%20FULL%20THESIS%20by%20TAYYABA%20AKRAM%20cut.pdf
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spelling	my-usm-ep.555712022-11-09T02:19:31Z B-Splines Based Finite Difference Schemes For Fractional Partial Differential Equations 2020-02 Akram, Tayyaba QA1-939 Mathematics Fractional partial differential equations (FPDEs) are considered to be the extended formulation of classical partial differential equations (PDEs). Several physical models in certain fields of sciences and engineering are more appropriately formulated in the form of FPDEs. FPDEs in general, do not have exact analytical solutions. Thus, the need to develop new numerical methods for the solutions of space and time FPDEs. This research focuses on the development of new numerical methods. Two methods based on B-splines are developed to solve linear and non-linear FPDEs. The methods are extended cubic B-spline approximation (ExCuBS) and new extended cubic B-spline approximation (NExCuBS). Both methods have the same basis functions but for the NExCuBS, a new approximation is used for the second order space derivative. 2020-02 Thesis http://eprints.usm.my/55571/ http://eprints.usm.my/55571/1/Pages%20from%20FULL%20THESIS%20by%20TAYYABA%20AKRAM%20cut.pdf application/pdf en public phd doctoral Universiti Sains Malaysia Pusat Pengajian Sains Matematik (School of Mathematical Sciences)
institution	Universiti Sains Malaysia
collection	USM Institutional Repository
language	English
topic	QA1-939 Mathematics
spellingShingle	QA1-939 Mathematics Akram, Tayyaba B-Splines Based Finite Difference Schemes For Fractional Partial Differential Equations
description	Fractional partial differential equations (FPDEs) are considered to be the extended formulation of classical partial differential equations (PDEs). Several physical models in certain fields of sciences and engineering are more appropriately formulated in the form of FPDEs. FPDEs in general, do not have exact analytical solutions. Thus, the need to develop new numerical methods for the solutions of space and time FPDEs. This research focuses on the development of new numerical methods. Two methods based on B-splines are developed to solve linear and non-linear FPDEs. The methods are extended cubic B-spline approximation (ExCuBS) and new extended cubic B-spline approximation (NExCuBS). Both methods have the same basis functions but for the NExCuBS, a new approximation is used for the second order space derivative.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Akram, Tayyaba
author_facet	Akram, Tayyaba
author_sort	Akram, Tayyaba
title	B-Splines Based Finite Difference Schemes For Fractional Partial Differential Equations
title_short	B-Splines Based Finite Difference Schemes For Fractional Partial Differential Equations
title_full	B-Splines Based Finite Difference Schemes For Fractional Partial Differential Equations
title_fullStr	B-Splines Based Finite Difference Schemes For Fractional Partial Differential Equations
title_full_unstemmed	B-Splines Based Finite Difference Schemes For Fractional Partial Differential Equations
title_sort	b-splines based finite difference schemes for fractional partial differential equations
granting_institution	Universiti Sains Malaysia
granting_department	Pusat Pengajian Sains Matematik (School of Mathematical Sciences)
publishDate	2020
url	http://eprints.usm.my/55571/1/Pages%20from%20FULL%20THESIS%20by%20TAYYABA%20AKRAM%20cut.pdf
_version_	1776101094530744320

B-Splines Based Finite Difference Schemes For Fractional Partial Differential Equations

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