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

  • MH Kabir Department of Mathematics, Jahangirnagar University, Savar, Dhaka
  • A Afroz IUBAT-International University of Business Agriculture and Technology, Uttara, Dhaka
  • LS Andallah Department of Mathematics, Jahangirnagar University, Savar, Dhaka
Keywords: Finite difference scheme, Macroscopic, Well-posed-ness, Stability

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

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Abstract
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Published
2012-12-21
How to Cite
Kabir, M., Afroz, A., & Andallah, L. (2012). A finite difference scheme for a macroscopic traffic flow model based on a nonlinear density-velocity relationship. Bangladesh Journal of Scientific and Industrial Research, 47(3), 339-346. https://doi.org/10.3329/bjsir.v47i3.13070
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