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 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

Cubic Trigonometric B-Spline Approach to Numerical Solution of Wave Equation

The generalized wave equation models various problems in sciences and engineering. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline for the approximate solution of wave equation is developed. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Von Neumann stability analysis is used to analyze the proposed method. Two problems are discussed to exhibit the feasibility and capability of the method. The absolute errors and maximum error are computed to assess the performance of the proposed method. The results were found to be in good agreement with known solutions and with existing schemes in literature

Cubic Trigonometric B-Spline Approach to Numerical Solution of Wave Equation

The generalized wave equation models various problems in sciences and engineering. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline for the approximate solution of wave equation is developed. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Von Neumann stability analysis is used to analyze the proposed method. Two problems are discussed to exhibit the feasibility and capability of the method. The absolute errors and maximum error are computed to assess the performance of the proposed method. The results were found to be in good agreement with known solutions and with existing schemes in literature

Shortest path technique for switching in a mesh network

Switching is a technique to route data and instructions between pairs of source-destination nodes or among multiple nodes for broadcast communication. We realized that the shortest path problem has a wide application in the design of networks. Therefore, in this paper, we present a mesh network as our switching mechanism for computing the shortest path between the source and destination in our simulation model, developed using C++ on the Windows environment. The Floyd-Warshall algorithm is applied in finding the shortest path in all-pairs nodes

Cubic Trigonometric B-Spline Approach to Numerical Solution of Wave Equation

The generalized wave equation models various problems in sciences and engineering. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline for the approximate solution of wave equation is developed. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Von Neumann stability analysis is used to analyze the proposed method. Two problems are discussed to exhibit the feasibility and capability of the method. The absolute errors and maximum error are computed to assess the performance of the proposed method. The results were found to be in good agreement with known solutions and with existing schemes in literature

Cubic Trigonometric B-Spline Approach to Numerical Solution of Wave Equation

The generalized wave equation models various problems in sciences and engineering. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline for the approximate solution of wave equation is developed. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Von Neumann stability analysis is used to analyze the proposed method. Two problems are discussed to exhibit the feasibility and capability of the method. The absolute errors and maximum error are computed to assess the performance of the proposed method. The results were found to be in good agreement with known solutions and with existing schemes in literature

Application of Hybrid Cubic B-Spline Collocation Approach for Solving a Generalized Nonlinear Klien-Gordon Equation

The generalized nonlinear Klien-Gordon equation is important in quantum mechanics and related fields. In this paper, a semi-implicit approach based on hybrid cubic B-spline is presented for the approximate solution of the nonlinear Klien-Gordon equation. The usual finite difference approach is used to discretize the time derivative while hybrid cubic B-spline is applied as an interpolating function in the space dimension. The results of applications to several test problems indicate good agreement with known solutions

Cubic Trigonometric B-Spline Approach to Numerical Solution of Wave Equation

The generalized wave equation models various problems in sciences and engineering. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline for the approximate solution of wave equation is developed. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Von Neumann stability analysis is used to analyze the proposed method. Two problems are discussed to exhibit the feasibility and capability of the method. The absolute errors and maximum error are computed to assess the performance of the proposed method. The results were found to be in good agreement with known solutions and with existing schemes in literature

Cubic Trigonometric B-Spline Approach to Numerical Solution of Wave Equation

The generalized wave equation models various problems in sciences and engineering. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline for the approximate solution of wave equation is developed. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Von Neumann stability analysis is used to analyze the proposed method. Two problems are discussed to exhibit the feasibility and capability of the method. The absolute errors and maximum error are computed to assess the performance of the proposed method. The results were found to be in good agreement with known solutions and with existing schemes in literature

Cubic Trigonometric B-Spline Approach to Numerical Solution of Wave Equation

The generalized wave equation models various problems in sciences and engineering. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline for the approximate solution of wave equation is developed. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Von Neumann stability analysis is used to analyze the proposed method. Two problems are discussed to exhibit the feasibility and capability of the method. The absolute errors and maximum error are computed to assess the performance of the proposed method. The results were found to be in good agreement with known solutions and with existing schemes in literature