is not smooth, but proceeds discontinuously and therefore this phase is difficult to follow numerically. Even if the number of grid points is increased considerably, the step-wise motion could not be suppressed totally. Consequently it is very difficult to determine in advance when the next H-rich shell is mixed into the hotter regions and the appropriate next time-step is nearly impossible to determine. Using time-steps too large shortly before the onset of mixing, the violent H-burning phase may be missed, while time-steps too short make the computation of the whole phase very time consuming.

The reason for this behaviour is that the stellar evolution program calculates the physical structure of a model at a certain epoch and afterwards uses this structure (in particular the density- and temperature-profile) to calculate the chemical evolution during a certain time interval following. The solution of all the stellar structure equations (physical as well as chemical variables) in a common scheme would be possible, but it is not advisable, since during this phase already a large number of iterations ($\ga 40$) are needed for the physical variables alone. Including the chemical evolution in the solution of the stellar structure would increase the computing time by 