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

Authors

  • 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

DOI:

https://doi.org/10.3329/bjsir.v47i3.13070

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

Downloads

Download data is not yet available.
Abstract
143
PDF
121

Downloads

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

Issue

Vol. 47 No. 3 (2012)

Section

Articles

License

Bangladesh Council of Scientific and Industrial Research (BCSIR) holds the copyright to all contents published in Bangladesh Journal of Scientific and Industrial Research (BJSIR). A copyright transfer form should be signed by the author(s) and be returned to BJSIR.

The entire contents of the BJSIR are protected under Bangladesh Council of Scientific and Industrial Research (BCSIR) copyrights.

Creative Commons Licence
BJSIR is an open access journal, and articles are distributed under the terms of the Creative Commons Attribution-NonCommercial License (CC BY-NC) Creative Commons Attribution-NonCommercial 4.0 International License which allows others remix, tweak, and build upon the articles non-commercially, and although their new works must also acknowledge and be non-commercial, they don’t have to license their derivative works on the same terms.