Lax-Friedrich Scheme for the Numerical Simulation of a Traffic Flow Model Based on a Nonlinear Velocity Density Relation

Show more

References

[1] Klar, A., Kuhne, R.D. and Wegener, R. (1996) Mathematical Models for Vehicular Traffic. Technical University of Kaiserslautern, Kaiserslautern.

[2] Bretti, G., Natalini, R. and Piccoli, B. (2007) A Fluid-Dynamic Traffic Model on Road Networks. Compute Methods Eng., 14, 139-172.

[3] Lighthill, M.J. and Whitham, G.B. (1955) On Kinematic Waves, I, Flood Movement in Long Rivers. Proceedings of the Royal Society of London A, 229, 281-316.

http://dx.doi.org/10.1098/rspa.1955.0088

[4] Lighthill, M.J. and Whitham, G.B. (1955) A Theory of Traffic Flow on Long Crowded Roads. Proceedings of the Royal Society of London A, 229, 317-345.

http://dx.doi.org/10.1098/rspa.1955.0089

[5] Haberman, R. (1977) Mathematical Models. Prentice-Hall, Inc., Delhi.

[6] Wegener, R. and Klar, A. (1995) A Kinetic Model for Vehicular Traffic Derived from a Stochastic Microscopic Model. Berichte der Arbeitsgruppe Technomathematik 138, Universitat, Kaiserslautern.

[7] Andallah, L.S., Ali, S., Gani, M.O., Pandit, M.K. and Akhter, J. (2009) A Finite Difference Scheme for a Traffic Flow Model Based on a Linear Velocity-Density Function. Jahangirnagar University Journal of Science, 32, 61-71.

[8] Kabir, M.H., Gani, M.O. and Andallah, L.S. (2010) Numerical Simulation of a Mathematical Traffic Flow Model Based on a Non-Linear Velocity-Density Function. Journal of Bangladesh Academy of Sciences, 34, 15-22.

[9] Leveque, R.J. (1992) Numerical Methods for Conservation Laws. 2nd Edition, Springer, Berlin.

[10] Daganzo, C.F. (1995) A Finite Difference Approximation of the Kinematic Wave Model of Traffic Flow. Transportation Research Part B: Methodological, 29, 261-276.