Stability and Convergence of Time Marching Methods in Scattering Problems

Abstract

We consider the stability and convergence of time marching methods for solving transient scattering problems. In such methods discretization errors tend to accumulate rapidly and grow exponentially in time. In this paper we present conditions which ensure that the effect of these errors can be made arbitrarily small on any finite time interval. The results are applicable to a wide range of scattering problems, such as two and three dimensional acoustic and electromagnetic problems.