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. We explain how this fact is related to 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 also show that, and explain why, for the MoC employing some other ODE solvers, stability of the modes may be unaffected by the BC.
['Taras I. Lakoba', 'Zihao Deng']
Stability analysis of the numerical Method of characteristics applied to energy-preserving systems. Part II: Nonreflecting boundary conditions