B-Spline Collocation Approach For Solving Partial Differential Equations

• 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; http://eprints.usm.my/31880/
• Institution: Universiti Sains Malaysia

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.