A front tracking method for a strongly coupled PDE-ODE system with moving density constraints in traffic flow

DOI10.3934/DCDSS.2014.7.435zbMath1292.90078OpenAlexW2013697370MaRDI QIDQ2438032

Maria Laura Delle Monache, Paola Goatin

Publication date: 10 March 2014

Published in: Discrete and Continuous Dynamical Systems. Series S (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdss.2014.7.435

zbMATH Keywords

numerical simulationstraffic flow modelingconservation laws with constraintsfront-tracking methodsPDE-ODE model

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Hyperbolic conservation laws (35L65) Traffic problems in operations research (90B20) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99)

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Cites Work

• Unnamed Item
• Unnamed Item
• Mixed systems: ODEs-balance laws
• The Godunov scheme for scalar conservation laws with discontinuous bell-shaped flux functions
• Finite volume schemes for locally constrained conservation laws
• Convergent and conservative schemes for nonclassical solutions based on kinetic relations. I
• Computational method for propagating phase boundaries
• General constrained conservation laws. Application to pedestrian flow modeling
• Moving Bottlenecks in Car Traffic Flow: A PDE-ODE Coupled Model
• First order quasilinear equations with boundary conditions
• A Tracking Algorithm for Car Paths on Road Networks
• A Hölder continuous ODE related to traffic flow
• Shock Waves on the Highway
• On kinematic waves II. A theory of traffic flow on long crowded roads

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