We discuss numerical stabilisation of dynamics governed by nonlinear hyperbolic conservation laws through feedback boundary conditions. Using a discrete Lyapunov function we prove exponential decay of the discrete solution to first– order finite volume schemes in conservative form. Decay rates are established for a large class of finite volume schemes including the Lax–Friedrichs scheme. Theore...

We develop new high-order accurate upwind schemes for the wave equation in second-order form. These schemes are developed directly for the equations in second-order form, as opposed to transforming the equations to a first-order hyperbolic system. The schemes are based on the solution to a local Riemann-type problem that uses d’Alembert’s exact solution. We construct conservative finite differe...

We consider the approximation by multidimensional finite volume schemes of the transport of an initial measure by a Lipschitz flow. We first consider a scheme defined via characteristics, and we prove the convergence to the continuous solution, as the time-step and the ratio of the space step to the time-step tend to zero. We then consider a second finite volume scheme, obtained from the first ...

In this paper we suggest an explicit finite-difference scheme for numerical simulation of the Cauchy problem with integro-differential nonlinear equation that describes oscillatory process friction and memory (hereditarity), corresponding local initial conditions. The problems approximation, stability, convergence proposed are investigated. results computer experiments implement scheme, confirm...