Some Remarks on Convergence and Stability in Ray-Tracing Calculations

A class of finite difference methods, the linear one-cell functional methods, is introduced, and observed to encompass the vast majority of spatial approximations used in one-dimensional transport theory. It is noted that, under minimal additional assumptions, these methods satisfy the classical result, valid for one-step finite difference approximations to initial value problems, that consistency implies both convergence and stability. This explains the observed absence of nonconvergence and instability from ray-tracing calculations, and also indicates the limitations of this result.