Inhomogeneous conditions at open boundaries for wave propagation problems (Q1101189)

Wave propagation problems with absorbing boundary conditions are treated. The approximations are known to become weakly unstable. This difficulty is more pronounced for inhomogeneous boundary conditions. In this paper this is further investigated and it is shown that reasonable estimates can still be obtained if the solution is smooth. An implementation of high-order conditions for first-order systems is described. The purpose of this paper is to illuminate the influence of the weak instabilities inherent with higher-order derivatives in the boundary conditions, and how to remove them. These principles can also be applied to problems which are not of pure wave-propagation type.