Constructing non-reflecting boundary conditions using summation-by-parts in time

In this paper we provide a new approach for constructing non–reflecting boundary conditions. The boundary conditions are based on summation– by–parts operators and derived without Laplace transformation in time. We prove that the new non–reflecting boundary conditions yield a well-posed problem and that the corresponding numerical approximation is unconditionally stable. The analysis is demonstrated on a hyperbolic system in two space dimensions, and the theoretical results are confirmed by numerical experiments.