A numerical solution of traffic flow problem for one lane roadway

Abstract

This research is conducted to model flow of traffic on a one lane roadway by partial differential equation (PDE). Then, Finite Difference Method (FDM) is used to solve one-dimensional traffic flow equation. The Finite Difference Method involved is forward difference and central difference. In this problem, the density of cars with fixed ends is considered. The finite difference method (FDM) proceeds by replacing the derivatives in the traffic flow equations by finite difference approximations. This gives a large algebraic system of equations to be solved, which can be solved easily in mathematics software. MATLAB Distributed Computing R2010a software is used to perform the computational experiment while Microsoft Excel is used toillustrated the graphs. In this research, the effect of different step space, h and step time, k are investigated. Besides, comparison between finite difference solutions and analytical solutions will determine the accuracy of finite difference method (FDM).