Initial stepsize
The initial stepsize h0 must be, in principle, beyond the
above reported stepsize. In the human-expert mode, the user can
set the initial stepsize to any value (ignoring the restrictions).
Interesting tests can be made in this way in order to demonstrate
the importance of respecting the stability and accuracy conditions.
If the user do not respect the upper limit of the stepsize due to the
stability condition it is more probably that some of the
components of the approximate solution will grown unexpected
(the computation process will be automatically stopped and an
error message will appear; warning messages will appear also at
the begin of the computation process if some restriction of the
stepsize is not respected). If the user do not respect the upper limit
of the stepsize due to the accuracy condition, it is possible that the
computation process will be finished with success, but the estimated error
will be much great than the expected one.
Therefore, it is indicated that the user will select an initial
stepsize which is under the reported limits. This field is useful
to select an initial stepsize for a constant stepsize method
so that after a specific number of steps with this stepsize
the end of the integration interval will be reached exactly
(the length of the integration interval is a multiple of the
stepsize). Each modification in the initial stepsize will
automatically modifies the number of steps and the
estimated computation time.
Example for the method DIRK4 applied to the system B1.