In this study, we examine the effect of boundary conditions, both inflow and outflow, on the predicted flow fluctuations in a supersonic jet entering into a subsonic outer flow. Various boundary conditions are used to compute the flowfield of a laminar axisymmetric jet excited at the inflow by a disturbance given by the corresponding eigenfunction of the linearized stability equations. Our goal is to determine the suitability of these conditions for computations of time-dependent flows. We solve the full time-dependent Navier-Stokes equations by a high-order numerical scheme. For very small excitations, the computed growth of the modes closely corresponds to that predicted by the linear theory. We then vary the excitation level and examine the effect of the boundary conditions in the nonlinear flow regime.