Numerical Simulation of Diffusion Type Traffic Flow Model Using Second-Order Lax-Wendroff Scheme Based on Exponential Velocity Density Function

Abstract

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 so lution of the diffusion-type traffic flow model is very complicated to ap prox imate 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 ex plicit 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 diffu sion type traffic flow model is suitable for the congested area and shows a better fit in traffic - congested region s .