The following is a description of the solution strategy as implemented in Ansys Polyflow.
Calculate the predicted value
using an explicit
scheme: 
(29–11)
Calculate the corrected value
using an implicit scheme: Initialize
. Solve for
with the iteration 
(29–12)
This equation is identical in form to Equation 29–8.
If this converges, continue to step 3. Otherwise, divide
by 2, and
return to step 1, unless 
is less than
the minimum step size, in which case stop the calculation.
Accept or reject the corrected value on the basis of the precision:
(29–13)
Otherwise, reject
and return to step 1. Estimate the next time step using Equation 29–9. Compare the new value of
with 
and keep the smaller value. Return to step 1 for the solution at time
.
These steps are repeated until the upper time limit is reached, 
falls below the minimum step size (Step 2.c.), or
the maximum number of successful steps is reached.