Nonlinear hydrodynamic models of traffic flow modelling and mathematical problems

Mathematical and Computer Modelling

Volumn 29, Issue 7, 1999, Pages 83-95

  De Angelis, E ^a  

^a POLITECNICO DI TORINO   (Italy)

Author keywords

Evolution equations; Nonlinear hydrodynamics; Nonlinear sciences; Traffic models

Indexed keywords

EID: 0033119901     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0895-7177(99)00064-3     Document Type: Article

References (16)

1. 1. Y. Prigogine and R. Hermann, Kinetic Theory of Vehicular Traffic, Elsevier, (1971).
2. 2. W. Leutzback, Introduction to the Theory of Traffic Flow, Springer, Berlin, (1988).
3. 3. A. Klar, R.D. Küne and R. Wegener, Mathematical models for vehicular traffic, Surveys Math. Ind. 6, 215-232 (1996).
4. 4. G.B. Whitham, Linear and Nonlinear Waves, Wiley & Sons, (1974).
5. 5. N. Bellomo, Nonlinear models and problems in applied sciences: From differential quadrature to generalized collocation methods, Mathl. Comput. Modelling 26 (4), 13-34 (1997).
6. 6. B.S. Kerner and P. Konhäuser, Cluster effect in initially homogeneous traffic flow, Physical Review E 48, 2335-2348 (1993).
7. 3 AS 2, 91-112 (1992).
8. 3 AS 7, 385-404 (1997).
9. 3 AS 7, 1187-1212 (1997).
10. 10. P. Castagna and R. Cresto, Modelli di traffico: Sviluppo di software applicativo e problemi di simulazione, M.S. Dissertation, Department of Mathematics, Politecnico of Torino.
11. 11. N. Bellomo and L. Ridolfi, Solution of nonlinear initial-boundary value problems by Sinc collocation methods, Computers Math. Applic. 29 (4), 15-28 (1995).
12. 12. J. Lund and K. Bowers, Sinc Methods, SIAM, (1992).
13. 13. F. Stenger, Numerical Methods Based on Sinc and Analytic Functions, Springer, Berlin, (1993).
14. 14. N. Bellomo and L. Preziosi, Modelling Mathematical Methods and Scientific Computation, CRC Press, Boca Raton, FL, (1995).
15. 15. C. Bert and M. Malik, Differential quadrature method in computational mechanics, ASME Review 49, 1-27 (1996).
16. 16. N. Bellomo and M. Lo Schiavo, From the Boltzmann equation to generalized kinetic models in applied sciences, Mathl. Comput. Modelling 26 (7), 43-76 (1997).