40 research outputs found
On an Exchange Interaction Model for Quantum Transport: The Schrödinger–Poisson–Slater System
No full text
On the Schrödinger–Poisson–Slater System: Behavior of Minimizers, Radial and Nonradial Cases
No full textStability and convergence of second order backward differentiation schemes for parabolic Hamilton–Jacobi–Bellman equations
No full textValue iteration convergence of -monotone schemes for stationary Hamilton-Jacobi equations
No full textA High-Order Semi-Lagrangian/Finite Volume Scheme for Hamilton-Jacobi-Isaacs Equations
No full textInternational audienceWe present a numerical scheme for the approximation of Hamilton-Jacobi-Isaacs equations related to optimal control problems and differential games. In the first case, the Hamiltonian is convex with respect to the gradient of the solution, whereas the second case corresponds to a non convex (minmax) operator. We introduce a scheme based on the combination of semi-Lagrangian time discretization with a high-order finite volume spatial reconstruction. The high-order character of the scheme provides an efficient way towards accurate approximations with coarse grids. We assess the performance of the scheme with a set of problems arising in minimum time optimal control and pursuit-evasion games
