  Elementary integration methods for waveguides are compared. One using
non-local loading rules based on Heaviside step functions, one using input side
integration and one using integration of the output of traveling velocity
waves. We show that most approaches can be made consistent with the wave
equation in principle, under proper circumstances. Of all methods studied the
Heaviside method is the only method shown to not suffer from undesirable
numerical difficulties and amendable to standard waveguide loop filtering
practices, yet it gives incorrect results for Neumann boundary conditions. We
also discuss localized velocity excitations, time-limited input-side
excitations and the relation of loop filters to wave variable type.
