The great difficulties connected with the numerical solution of the steady compressible Navier-Stokes equations can be avoided if the steady flow is considered as the asymptotic form of a time-dependent flow, thus profiting from the techniques available for the numerical solution of initial value problems. In practice, the numerical procedure can imitate the natural development of the final steady flow in a shock tube. It is observed, however, that the accuracy and the consistency of the transient flow computations is here of no concern; this part of the calculations is merely fulfilling the function of an iteration procedure. This gives a great freedom in the choice of the numerical schemes, which therefore can be adjusted to fit, in the best way, the stability requirements. As a simple example of this technique, calculations have been performed of the one-dimensional formation of a standing shock in a divergent duct with initially supersonic flow when a back pressure is applied. Stability of the calculations is assured through the use of a suitable, conditionally stable, difference scheme. The results of the calculations show indeed that stability can be obtained in practice, provided certain precautions are taken in the application of the back pressure, and that the resulting flow converges to the expected mixed supersonic-subsonic flow with a standing shock. However, for sufficiently low viscosity the steady solution exhibits a wavy character with no counterpart in nature. These waves are analytically shown to appear whenever the space interval becomes larger than half the shock thickness.