Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 6

Publications

6 Cubic Trigonometric B-spline Approach to Numerical Solution of Wave Equation

Authors: Ahmad Izani Md. Ismail, Muhammad Abbas, Shazalina Mat Zin, Ahmad Abd. Majid

Abstract:

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.

Keywords: Finite Difference, Wave Equation, collocation method, cubic trigonometric B-spline

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5 Applications of High-Order Compact Finite Difference Scheme to Nonlinear Goursat Problems

Authors: Ahmad Izani Md. Ismail, Mohd Agos Salim Nasir

Abstract:

Several numerical schemes utilizing central difference approximations have been developed to solve the Goursat problem. However, in a recent years compact discretization methods which leads to high-order finite difference schemes have been used since it is capable of achieving better accuracy as well as preserving certain features of the equation e.g. linearity. The basic idea of the new scheme is to find the compact approximations to the derivative terms by differentiating centrally the governing equations. Our primary interest is to study the performance of the new scheme when applied to two Goursat partial differential equations against the traditional finite difference scheme.

Keywords: partial differential equation, Goursat problem, finite difference scheme, compact finite difference

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4 A Comparison of Some Splines-Based Methods for the One-dimensional Heat Equation

Authors: Ahmad Izani Md. Ismail, Joan Goh, Ahmad Abd. Majid

Abstract:

In this paper, collocation based cubic B-spline and extended cubic uniform B-spline method are considered for solving one-dimensional heat equation with a nonlocal initial condition. Finite difference and θ-weighted scheme is used for time and space discretization respectively. The stability of the method is analyzed by the Von Neumann method. Accuracy of the methods is illustrated with an example. The numerical results are obtained and compared with the analytical solutions.

Keywords: heat equation, Collocation based, Cubic Bspline, Extended cubic uniform B-spline

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3 Cubic Trigonometric B-Spline Applied to Linear Two-Point Boundary Value Problems of Order Two

Authors: Ahmad Izani Md. Ismail, Ahmad Abd. Majid, Nur Nadiah Abd Hamid

Abstract:

Linear two-point boundary value problems of order two are solved using cubic trigonometric B-spline interpolation method (CTBIM). Cubic trigonometric B-spline is a piecewise function consisting of trigonometric equations. This method is tested on some problems and the results are compared with cubic B-spline interpolation method (CBIM) from the literature. CTBIM is found to approximate the solution slightly more accurately than CBIM if the problems are trigonometric.

Keywords: Spline interpolation, trigonometric B-spline, two-point boundary valueproblem, cubic spline

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2 Extended Cubic B-spline Interpolation Method Applied to Linear Two-Point Boundary Value Problems

Authors: Ahmad Izani Md. Ismail, Ahmad Abd. Majid, Nur Nadiah Abd Hamid

Abstract:

Linear two-point boundary value problem of order two is solved using extended cubic B-spline interpolation method. There is one free parameters, λ, that control the tension of the solution curve. For some λ, this method produced better results than cubic B-spline interpolation method.

Keywords: B-spline, two-point boundary value problem, extendedcubic B-spline

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1 Dynamic Traffic Simulation for Traffic Congestion Problem Using an Enhanced Algorithm

Authors: Ahmad Izani Md. Ismail, Abdullah Zawawi Talib, Mohd. Azam Osman, Wong Poh Lee

Abstract:

Traffic congestion has become a major problem in many countries. One of the main causes of traffic congestion is due to road merges. Vehicles tend to move slower when they reach the merging point. In this paper, an enhanced algorithm for traffic simulation based on the fluid-dynamic algorithm and kinematic wave theory is proposed. The enhanced algorithm is used to study traffic congestion at a road merge. This paper also describes the development of a dynamic traffic simulation tool which is used as a scenario planning and to forecast traffic congestion level in a certain time based on defined parameter values. The tool incorporates the enhanced algorithm as well as the two original algorithms. Output from the three above mentioned algorithms are measured in terms of traffic queue length, travel time and the total number of vehicles passing through the merging point. This paper also suggests an efficient way of reducing traffic congestion at a road merge by analyzing the traffic queue length and travel time.

Keywords: Simulation, Dynamic, Traffic Congestion, fluid-dynamic, kinematic wave theory

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