A finite difference scheme for a macroscopic traffic flow model based on a nonlinear density-velocity relationship

Abstract

We consider a macroscopic traffic flow model tagged on a closure nonlinear density-velocity relationship yielding a quasi-linear first order (hyperbolic) partial differential equation (PDE) as an initial boundary value problem (IBVP). We present the analytic solution of the PDE which is in implicit form. We describe the derivation of a finite difference scheme of the IBVP which is a first order explicit upwind difference scheme. We establish the well-posed-ness and stability condition of the finite difference scheme. To implement the numerical scheme we develop computer program using MATLAB programming language in order to verify some qualitative behaviors for various traffic parameters. DOI: http://dx.doi.org/10.3329/bjsir.v47i3.13070 Bangladesh J. Sci. Ind. Res. 47(3), 339-346 2012

Numerical Solution of a Multilane Traffic Flow Model

“…In order to investigate efficient numerical simulation of a single-lane highway traffic flow model by using finite difference scheme we have studied the works [7], [8], [10]. In this article, we extend the work for a multilane traffic flow model (macroscopic type) appended with a linear density-velocity relationship.…”