Improved Error Bounds for Dirichlet-to-Neumann Absorbing Boundaries
  It has long been known how to construct radiation boundary conditions for the time dependent wave equation. Although arguments suggesting that they are accurate have been given, it is only recently that rigorous error bounds have been proved. Previous estimates show that the error caused by these methods behaves like epsilon C exp(gamma t) for any gamma > 0. We improve these results and show that the error behaves like epsilon t^2. 
Charles Siegel, Avy Soffer and Chris Stucchio