Abstract
AbstractTime‐domain integral equation analyses are prone to instabilities, in a range of applications areas including acoustics, electrodynamics and elastodynamics, and a variety of retrospective averaging schemes have been proposed to improve matters. In this paper, we investigate stability behaviour, in parallel, in electrodynamic and elastodynamic cases. It is observed empirically that the tendency to instability is increased as the treatment becomes more nearly explicit. The timestepping procedure is recast in a recursive matrix formulation, and it is shown that it is the eigenvalues of this large matrix which determine the long‐term stability behaviour. This treatment is then extended to cover general averaging schemes, allowing the likely effectiveness of such schemes to be assessed. Simple modelling rules, which for all practical purposes will ensure stability, are presented. Copyright © 2002 John Wiley & Sons, Ltd.
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