On the behaviour of time discretisations of the electric field integral equation

We derive a separation of variables solution for time-domain electromagneti c scattering from a perfectly conducting infinite flat plate. The time depe ndent part of the equations are then used as a model problem in order to st udy the effects of various time discretisations on the full scattering prob lem. We examine and explain how exponential and polynomial instabilities ar ise in the approximation schemes, and show that the time averaging which is often used in an attempt to stabilise solutions of the full problem acts t o destabilise some of the schemes. Our results show that two of the time di scretisations can produce good results when coupled with a space-exact appr oximation, and indicate that they will be useful when coupled with an accur ate enough spatial approximation. (C) 2000 Elsevier Science Inc. All rights reserved.