Exact nonreflecting boundary conditions are considered for exterior th
ree-dimensional lime-dependent wave problems. These include a nonlocal
condition for acoustic waves based on Kirchhoff's formula, orginally
proposed by L. Ting and M. J. Miksis (J. Acoust. Sec. Am. 80, 1825 (19
86), and an analogous condition for elastic waves. These conditions ar
e computationally attractive in that their temporal nonlocality is lim
ited to a fixed amount of past information. However, when a standard n
ondissipative finite difference stencil is used as the interior scheme
, a long-time instability is exhibited in the numerical solution. This
instability is analyzed for a simple one-dimensional model problem. I
t is eliminated once the standard interior scheme is replaced by the d
issipative Lax-Wendroff scheme. In this case stability is demonstrated
experimentally, and it is also established theoretically in the one-d
imensional case. (C) 1995 Academic Press, Inc.