  A version of the STARS stellar evolution code has been developed that uses a
non-simultaneous solution of the equations of stellar structure and evolution.
In all other respects it is identical to the normal, fully simultaneous
version. It is therefore possible to test the dependence of the solution on how
the equations are solved. Two cases are investigated: a 5Msol and a 3Msol star,
both of metallicity Z=0.02. Prior to the asymptotic giant branch, the models
are almost identical. However once thermal pulses start, the two methods of
solution yield diverging results with the non-simultaneous technique predicting
longer interpulse periods. This is traced to difficulties associated with
hydrogen burning caused by the use of a moving mesh. It is shown that, with
careful control of the temporal resolution, the results of the simultaneous
technique can be recovered.
