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

Taras I. Lakoba, Zihao Deng

Abstract: 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.