B-Spline Collocation Approach For Solving Partial Differential Equations

Fungsi-fungsi splin-B dan trigonometri splin-B telah digunakan secara meluas dalam Rekabentuk Geometri Berbantu Komputer (RGBK) sebagai alat untuk menjana lengkung dan permukaan. Kelebihan fungsi-fungsi secara sepotong ini ialah ciri sokongan setempat dimana fungsi-fungsi ini dikatakan mempunyai sok...

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Main Author:	Mat Zin, Shazalina
Format:	Thesis
Language:	English
Published:	2016
Subjects:	QA1 Mathematics (General)
Online Access:	http://eprints.usm.my/31880/1/SHAZALINA_BINTI_MAT_ZIN_24%28NN%29.pdf
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spelling	my-usm-ep.318802019-04-12T05:25:27Z B-Spline Collocation Approach For Solving Partial Differential Equations 2016-01 Mat Zin, Shazalina QA1 Mathematics (General) Fungsi-fungsi splin-B dan trigonometri splin-B telah digunakan secara meluas dalam Rekabentuk Geometri Berbantu Komputer (RGBK) sebagai alat untuk menjana lengkung dan permukaan. Kelebihan fungsi-fungsi secara sepotong ini ialah ciri sokongan setempat dimana fungsi-fungsi ini dikatakan mempunyai sokongan dalam selang tertentu. Disebabkan oleh ciri ini, splin-B telah digunakan untuk menjana penyelesaian-penyelesaian berangka bagi persamaan pembezaan separa linear dan tak linear. Dalam tesis ini, dua jenis fungsi asas splin-B dipertimbangkan. Ianya adalah fungsi asas splin-B dan fungsi asas trigonometri splin-B. Pembangunan fungsi-fungsi ini untuk peringkat-peringkat yang berbeza dilaksanakan. Satu fungsi baru dipanggil fungsi asas hibrid splin-B dibangunkan dimana satu parameter digabungkan bersama fungsi-fungsi asas splin-B dan trigonometri splin-B diperkenalkan. Kaedah-kaedah kolokasi berdasarkan fungsi-fungsi asas tersebut dan hampiran beza terhingga dibangunkan. The B-spline and trigonometric B-spline functions were used extensively in Computer Aided Geometric Design (CAGD) as tools to generate curves and surfaces. An advantage of these piecewise functions is its local support properties where the functions are said to have support in specific interval. Due to this properties, B-splines have been used to generate the numerical solutions of linear and nonlinear partial differential equations. In this thesis, two types of B-spline basis function are considered. These are B-spline basis function and trigonometric B-spline basis function. The development of these functions for different orders is carried out. A new function called hybrid B-spline basis function is developed where a new parameter incorporated with B-spline and trigonometric B-spline basis functions is introduced. Collocation methods based on the proposed basis functions and finite difference approximation are developed. 2016-01 Thesis http://eprints.usm.my/31880/ http://eprints.usm.my/31880/1/SHAZALINA_BINTI_MAT_ZIN_24%28NN%29.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 Mathematics (General)
spellingShingle	QA1 Mathematics (General) Mat Zin, Shazalina B-Spline Collocation Approach For Solving Partial Differential Equations
description	Fungsi-fungsi splin-B dan trigonometri splin-B telah digunakan secara meluas dalam Rekabentuk Geometri Berbantu Komputer (RGBK) sebagai alat untuk menjana lengkung dan permukaan. Kelebihan fungsi-fungsi secara sepotong ini ialah ciri sokongan setempat dimana fungsi-fungsi ini dikatakan mempunyai sokongan dalam selang tertentu. Disebabkan oleh ciri ini, splin-B telah digunakan untuk menjana penyelesaian-penyelesaian berangka bagi persamaan pembezaan separa linear dan tak linear. Dalam tesis ini, dua jenis fungsi asas splin-B dipertimbangkan. Ianya adalah fungsi asas splin-B dan fungsi asas trigonometri splin-B. Pembangunan fungsi-fungsi ini untuk peringkat-peringkat yang berbeza dilaksanakan. Satu fungsi baru dipanggil fungsi asas hibrid splin-B dibangunkan dimana satu parameter digabungkan bersama fungsi-fungsi asas splin-B dan trigonometri splin-B diperkenalkan. Kaedah-kaedah kolokasi berdasarkan fungsi-fungsi asas tersebut dan hampiran beza terhingga dibangunkan. The B-spline and trigonometric B-spline functions were used extensively in Computer Aided Geometric Design (CAGD) as tools to generate curves and surfaces. An advantage of these piecewise functions is its local support properties where the functions are said to have support in specific interval. Due to this properties, B-splines have been used to generate the numerical solutions of linear and nonlinear partial differential equations. In this thesis, two types of B-spline basis function are considered. These are B-spline basis function and trigonometric B-spline basis function. The development of these functions for different orders is carried out. A new function called hybrid B-spline basis function is developed where a new parameter incorporated with B-spline and trigonometric B-spline basis functions is introduced. Collocation methods based on the proposed basis functions and finite difference approximation are developed.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Mat Zin, Shazalina
author_facet	Mat Zin, Shazalina
author_sort	Mat Zin, Shazalina
title	B-Spline Collocation Approach For Solving Partial Differential Equations
title_short	B-Spline Collocation Approach For Solving Partial Differential Equations
title_full	B-Spline Collocation Approach For Solving Partial Differential Equations
title_fullStr	B-Spline Collocation Approach For Solving Partial Differential Equations
title_full_unstemmed	B-Spline Collocation Approach For Solving Partial Differential Equations
title_sort	b-spline collocation approach for solving partial differential equations
granting_institution	Universiti Sains Malaysia
granting_department	Pusat Pengajian Sains Matematik (School of Mathematical Sciences)
publishDate	2016
url	http://eprints.usm.my/31880/1/SHAZALINA_BINTI_MAT_ZIN_24%28NN%29.pdf
_version_	1747820501953150976

B-Spline Collocation Approach For Solving Partial Differential Equations

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