  We show that imposition of non-periodic, in place of periodic, boundary
conditions (BC) can alter stability of modes in the Method of characteristics
(MoC) employing certain ordinary-differential equation (ODE) numerical solvers.
Thus, using non-periodic BC may render some of the MoC schemes stable for most
practical computations, even though they are unstable for periodic BC. This
fact contradicts a statement, found in some literature, that an instability
detected by the von Neumann analysis for a given numerical scheme implies an
instability of that scheme with arbitrary (i.e., non-periodic) BC. We explain
the mechanism behind this contradiction. We also show that, and explain why,
for the MoC employing some other ODE solvers, stability of the modes may be
unaffected by the BC.
