Numerical simulation of macroscopic continuum traffic models
Tài liệu tham khảo
Ansorge, 1990, What does the entropy condition mean in traffic flow theory?, Transpn. Res., 24B, 133, 10.1016/0191-2615(90)90024-S
Babcock, 1984, Role of adaptive discretization in a freeway simulation model, Transpn. Res. Rec., 971, 80
Chakravarthy, 1983, High resolution applications of the Osher upwind scheme for the Euler equations
Engquist, 1981, One sided difference approximations for nonlinear conservation laws, Maths. Comp., 36, 321, 10.1090/S0025-5718-1981-0606500-X
Glaister, 1988, Riemann solutions of the shallow water equations, Journal of Hydraulic Research, 26, 293, 10.1080/00221688809499213
Glaister, 1990, Flux-difference splitting for inviscid, real gases with non-equilibrium chemistry, Computers Maths. Applic., 20, 45, 10.1016/0898-1221(90)90029-J
Gear, 1971
Harten, 1983, High resolution schemes for hyperbolic conservation laws, Journal of Comp. Phys., 49, 357, 10.1016/0021-9991(83)90136-5
Harten, 1984, On a class of high resolution total-variation-stable finite-difference schemes, Siam J. Num Anal., 12, 1, 10.1137/0721001
Hindmarsh, 1972, Linear multistep methods for ordinary differential equations, Lawrence Livermore Laboratory Report
Huang, 1981, Pseudo-unsteady difference schemes for discontinuous solutions of steady-state, one-dimensional fluid dynamics problems, J. Compt. Physics, 42, 195, 10.1016/0021-9991(81)90239-4
Lax, 1954, Weak solution of non-linear hyperbolic equations and their numerical computations, Communs. Pure Appl. Math., 7, 159, 10.1002/cpa.3160070112
Lax, 1972, Hyperbolic systems of conservations laws and the mathematical theory of shock waves, SIAM Regional conference series in applied mathematics
LeVeque, 1990, A study of numerical methods for hyperbolic conservation laws with stiff source terms, Journal of Comp. Physics, 86, 187, 10.1016/0021-9991(90)90097-K
Lighthill, 1955, On kinetic waves II: A theory of traffic flow on crowded roads, Proc. R. Soc. Lond., A229, 317, 10.1098/rspa.1955.0089
Michalopoulos, 1980, Modeling of traffic flow at signalized links, Transpn. Sci., 12, 9, 10.1287/trsc.14.1.9
Michalopoulos, 1984, Analysis of interrupted traffic flow by finite difference methods, Transpn. Res., 18B, 409, 10.1016/0191-2615(84)90021-3
Michalopoulos, 1985, A freeway simulation program for microcomputers, 330
Michalopoulos, 1988, A numerical methodology for analyzing traffic flow at congested surface streets, Proc. 14th ARRB Conf., 173
Murman, 1974, Analysis of embedded shock waves calculated by relaxation methods, AIAA J., 12, 626, 10.2514/3.49309
Newell, 1989, Comments on traffic dynamics, Transpn. Res., 23B, 386, 10.1016/0191-2615(89)90015-5
Oleinik, 1957, Discontinuous solutions of nonlinear differential equations, Uspekhi Mat. Nauk., 12, 3
Osher, 1982, Upwind difference schemes for hyperbolic systems of conservation laws, Maths. Comp., 38, 339, 10.1090/S0025-5718-1982-0645656-0
Payne, 1971, Models of freeway traffic and control, Proceedings, Mathematics of Public Systems, Simulation Council, 1, 51
Payne, 1979, FREEFLO: A macroscopic simulation model of freeway traffic, Transpn. Res. Rec., 722, 68
Roe, 1981, Approximate reimann solvers, parameter vectors, and difference schemes, J. Comput. Physics, 43, 357, 10.1016/0021-9991(81)90128-5
Roe, 1983, Some contributions to the modeling of discontinuous flows
Roe, 1984, Efficient construction and utilisation of approximate Reimann solutions, vI
Roe, 1986, Upwind differencing schemes for hyperbolic conservation laws with source terms, Lectures Notes in Maths., 1270, 41, 10.1007/BFb0078316
Ross, 1988, Traffic dynamics, Transpn. Res., 22B, 421, 10.1016/0191-2615(88)90023-9
Ross, 1989, Response to Newell, Transpn. Res., 23B, 390, 10.1016/0191-2615(89)90016-7
Sweby, 1984, High resolution schemes using flux limiters for hyperbolic conservation laws, Siam J. Numer. Anal, 21, 995, 10.1137/0721062
Van Leer, 1974, Towards the ultimate conservative difference schemes II, monotonicity and conservation combined in a second order scheme, J. Compt. Physics, 14, 361, 10.1016/0021-9991(74)90019-9
Van Leer, 1979, Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method, J. Comp. Pys., 23, 263, 10.1016/0021-9991(77)90094-8
Van Leer, 1984, On the relation between the upwind-differencing schemes of Godunov, Engquist-Osher and Roe, SIAM J. Sci. Stat. Comput., 5, 1, 10.1137/0905001