A semi-Lagrangian scheme for Hamilton-Jacobi equations on networks with application to traffic flow models
This work provides a stable numerical method for solving a class of PDEs on networks, which is relevant for traffic flow modeling and other network-based applications.
The authors develop a semi-Lagrangian scheme for Hamilton-Jacobi-Bellman equations on networks, proving convergence and error estimates, and validate it with numerical tests and traffic flow simulations.
We present a semi-Lagrangian scheme for the approximation of a class of Hamilton-Jacobi-Bellman equations on networks. The scheme is explicit and stable under some technical conditions. We prove a convergence theorem and some error estimates. Additionally, the theoretical results are validated by numerical tests. Finally, we apply the scheme to simulate traffic flows modeling problems.