  The classical (inviscid) stability analysis of shock waves is based on the
Lopatinski determinant, \Delta---a function of frequencies whose zeros
determine the stability of the underlying shock. A careful analysis of \Delta\
shows that in some cases the stable and unstable regions of parameter space are
separated by an open set of parameters. Zumbrun and Serre [Indiana Univ. Math.
J., 48 (1999) 937--992] have shown that, by taking account of viscous effects
not present in the definition of \Delta, it is possible to determine the
precise location in the open, neutral set of parameter space at which stability
is lost. In particular, they show that the transition to instability under
suitably localized perturbations is determined by an "effective viscosity"
coefficient. Here, in the simplest possible setting, we propose and implement
two new approaches toward the practical computation of this coefficient.
Moreover, in a special case, we derive an exact solution of the relevant
differential equations.
