We present a semi-Lagrangian scheme for the approximation of a class of Hamilton--Jacobi--Bellman (HJB) equations on networks. The scheme is explicit, consistent, and stable for large time steps. We prove a convergence result and two error estimates. For an HJB equation with space-independent Hamiltonian, we obtain a first order error estimate. In the general case, we provide, under a hyperbolic CFL condition, a convergence estimate of order one half. The theoretical results are discussed and validated in a numerical tests section.
A semi-Lagrangian scheme for Hamilton--Jacobi--Bellman equations on networks / Carlini, E.; Festa, A.; Forcadel, N.. - In: SIAM JOURNAL ON NUMERICAL ANALYSIS. - ISSN 0036-1429. - 58:6(2020), pp. 3165-3196. [10.1137/19M1260931]
A semi-Lagrangian scheme for Hamilton--Jacobi--Bellman equations on networks
E. CARLINI;
2020
Abstract
We present a semi-Lagrangian scheme for the approximation of a class of Hamilton--Jacobi--Bellman (HJB) equations on networks. The scheme is explicit, consistent, and stable for large time steps. We prove a convergence result and two error estimates. For an HJB equation with space-independent Hamiltonian, we obtain a first order error estimate. In the general case, we provide, under a hyperbolic CFL condition, a convergence estimate of order one half. The theoretical results are discussed and validated in a numerical tests section.File | Dimensione | Formato | |
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