  We study the stability properties of the Kidder-Scheel-Teukolsky (KST)
many-parameter formulation of Einstein's equations for weak gravitational waves
on flat space-time from a continuum and numerical point of view. At the
continuum, performing a linearized analysis of the equations around flat
spacetime, it turns out that they have, essentially, no non-principal terms. As
a consequence, in the weak field limit the stability properties of this
formulation depend only on the level of hyperbolicity of the system. At the
discrete level we present some simple one-dimensional simulations using the KST
family. The goal is to analyze the type of instabilities that appear as one
changes parameter values in the formulation. Lessons learnt in this analysis
can be applied in other formulations with similar properties.
