Author(s)

Mojammel Haque¹, Mariam Sultana², Laek Sazzad Andallah³

¹Department of Mathematics, Dhaka University of Engineering & Technology, Gazipur, Bangladesh.
²Department of Basic Science and Humanities, University of Asia Pacific, Dhaka, Bangladesh.
³Department of Mathematics, Jahangirnagar University, Dhaka, Bangladesh.

In order to control traffic congestion, many mathematical models have been used for several decades. In this paper, we study diffusion-type traffic flow model based on exponential velocity density relation, which provides a non-linear second-order parabolic partial differential equation. The analytical solution of the diffusion-type traffic flow model is very complicated to approximate the initial density of the Cauchy problem as a function of x from given data and it may cause a huge error. For the complexity of the analytical solution, the numerical solution is performed by implementing an explicit upwind, explicitly centered, and second-order Lax-Wendroff scheme for the numerical solution. From the comparison of relative error among these three schemes, it is observed that Lax-Wendroff scheme gives less error than the explicit upwind and explicit centered difference scheme. The numerical, analytical analysis and comparative result discussion bring out the fact that the Lax-Wendroff scheme with exponential velocity-density relation of diffusion type traffic flow model is suitable for the congested area and shows a better fit in traffic-congested regions.

Traffic Congestion, Diffusion Type Traffic Flow Model, Analytical Solution, Numerical Solution, Lax-Wendroff Scheme

Haque, M. , Sultana, M. and Andallah, L. (2023) Numerical Simulation of Diffusion Type Traffic Flow Model Using Second-Order Lax-Wendroff Scheme Based on Exponential Velocity Density Function. American Journal of Computational Mathematics, 13, 398-411. doi: 10.4236/ajcm.2023.133023.