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It is known that the stability of finite-difference models of hyperbolic initial-boundary value problems is connected with the propagation and reflection of parasitic waves. Here the waves point of view is applied to models containing two boundaries or interfaces, where repeated reflection of trapped wave packets is a potential new source of instability. Our analysis accounts for various known instability phenomena in a unified way and leads to several new results, three of which are asdoi:10.2307/2008125 fatcat:7wzbknhlqvamrod3btm56szfci