GPS-X Technical Reference

431 Miscellaneous
The Gear's Stiff routine is a self-tuning algorithm that adapts itself to rapidly
changing derivatives - in some cases though it might require excessive simulation
time to cross a discontinuity in the model. The Runge-Kutta-Fehlberg(1)
algorithm is exactly the opposite - it is very forgiving for discontinuities, but
experiences difficulties with steeper problems. A good compromise between
these two solvers is the Adams-Moulton algorithm. It is very robust and does not
give up easily but it is slower. The Runge-Kutta-Fehlberg(2) algorithm is almost
identical to Runge-Kutta-Fehlberg(1), but is more robust.
It is possible to monitor the step sizes used by the integration algorithm during a
run. You can either print the values to the Log window by entering the following
command at the command line in the Simulation Control window: output
truecssitg or place the variable truecssitg on an output graph. You can select
truecssitg for display in the
General Data > System > Display Variables > General program variables form
(it is labeled as Average integration step size). The average integration step size
(truecssitg) is calculated over each communication interval. Start your
simulation using a small communication interval (~0.01 or less). Sharp drops in
truecssitg usually signal a discontinuity. Using the above method, the Sum of
absolute values of the derivatives (dsum) can also be checked for sharp changes.
If your simulation is slow you can find which variable makes the simulation slow
by selecting the Fullinfo option in the Options>Set up>Information menu of the
Simulation Control window, and running the simulation using either the dams-
Moulton or Gear’s Stiff integration algorithms. The error summary displayed at
the end of the run in the Log window will point to the variable that controls the
step size.
The integration of systems with low DO (dissolved oxygen) concentrations (in
the range of a few dozen micrograms) is time consuming because the integration
algorithm has to cut back on the step size or risk running into negative DO
values.
Sometimes the integration algorithms have difficulty at the start of a simulation.
In such cases the initial concentrations of the state variables may be
inappropriate, resulting in large initial derivative values. In this case the variable
step integration algorithms keep cutting back on the step size to go over this
initial bump. It may be helpful to use the steady-state solver to determine the
initial conditions.
GPS-X Technical Reference