A finite difference approximation of a non-equilibrium traffic flow model

2001 ◽  
Vol 35 (4) ◽  
pp. 337-365 ◽  
Author(s):  
H.M. Zhang
Keyword(s):  
Finite Difference ◽  
Traffic Flow ◽  
Flow Model ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Traffic Flow Model ◽  
Non Equilibrium

scholarly journals A finite difference scheme for a fluid dynamic traffic flow model appended with two-point boundary condition

2012 ◽  
Vol 31 ◽  
pp. 43-52 ◽  
Author(s):  
MO Gani ◽  
MM Hossain ◽  
LS Andallah
Keyword(s):  
Boundary Condition ◽  
Finite Difference ◽  
Difference Scheme ◽  
Traffic Flow ◽  
Finite Difference Scheme ◽  
Flow Model ◽  
Fluid Dynamic ◽  
Point Boundary ◽  
Traffic Flow Model ◽  
First Order

A fluid dynamic traffic flow model with a linear velocity-density closure relation is considered. The model reads as a quasi-linear first order hyperbolic partial differential equation (PDE) and in order to incorporate initial and boundary data the PDE is treated as an initial boundary value problem (IBVP). The derivation of a first order explicit finite difference scheme of the IBVP for two-point boundary condition is presented which is analogous to the well known Lax-Friedrichs scheme. The Lax-Friedrichs scheme for our model is not straight-forward to implement and one needs to employ a simultaneous physical constraint and stability condition. Therefore, a mathematical analysis is presented in order to establish the physical constraint and stability condition of the scheme. The finite difference scheme is implemented and the graphical presentation of numerical features of error estimation and rate of convergence is produced. Numerical simulation results verify some well understood qualitative behavior of traffic flow.DOI: http://dx.doi.org/10.3329/ganit.v31i0.10307GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 31 (2011) 43-52

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

2012 ◽  
Vol 47 (3) ◽  
pp. 339-346 ◽  
Author(s):  
MH Kabir ◽  
A Afroz ◽  
LS Andallah
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Traffic Flow ◽  
Finite Difference Scheme ◽  
Flow Model ◽  
Traffic Flow Model ◽  
First Order ◽  
Velocity Relationship ◽  
Macroscopic Traffic Flow ◽  
Matlab Programming

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

Study on Discrete Autonomous Traffic Flow Model with Zero-Order Hold

CICTP 2020 ◽  
2020 ◽  
Author(s):  
Lidong Zhang ◽  
Wenxing Zhu ◽  
Mengmeng Zhang ◽  
Cuijiao Chen
Keyword(s):  
Traffic Flow ◽  
Flow Model ◽  
Zero Order ◽  
Traffic Flow Model
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