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We show that imposition of non-periodic, in place of periodic, boundaryconditions (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 mostpractical computations, even though they are unstable for periodic BC. Thisfact contradicts a statement, found in some literature, that an instabilitydetected by the von Neumann analysis for a given numerical scheme implies aninstability of that scheme with arbitrary (i.e., non-periodic) BC. We explainthe mechanism behind this contradiction. We also show that, and explain why,for the MoC employing some other ODE solvers, stability of the modes may beunaffected by the BC.

Stability analysis of the numerical Method of characteristics applied to  a class of energy-preserving systems. Part II: Nonreflecting boundary  conditions