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In article <1992Nov10.172608.25322@fys.ruu.nl> walsteyn@fys.ruu.nl (Fred Walsteijn) writes:

Fred>   In <KJELL.92Nov9164250@simplicity.Stanford.EDU>
Fred>   kjell@simplicity.Stanford.EDU (Kjell Gustafsson) writes: 
Fred>
Fred>   >The relation between the stepsize and the error may be quite different
Fred>   >than the normally assumed asymptotic form. Part of this "deviation"
Fred>   >has structure and can be modeled. By exploiting these models one
Fred>   >arrive at a stepsize selection rule that results in smoother stepsize
Fred>   >(and error) sequences as well as fewer stepsize rejections than the
Fred>
Fred>   Does this increase robustness of the error estimate in cases
Fred>   where the right hand side is discontinuous ??

No, not really! If you have a right hand side including
discontinuities you should use an integration method designed to
handle that. This normally requires you to supply some kind of
indicator function. The integration method applies a root finder to the
indicator function to resolve where the discontinuity occurs, and then
chooses an appropriate stepsize sequence to pass the discontinuity.
A good example of such a code is DDASRT written by Linda Petzold.

When dealing with discontinuous right hand sides it is important to be
careful in the modeling. For certain types of discontinuities one can
determine in beforehand at what time instance the discontinuity
occurs, e.g. discontinuous input signals, simulation of combined
sampled and continuous-time systems, etc. The simulation can then be
handled as a sequence of continuous problems.

Strategies that count on the stepsize control to resolve the problem
with discontinuities often lead to inefficiency (it may take a lot of
rejected steps to pass the discontinuity) or inaccuracy (some codes
will reduce the stepsize to a minimum value and then use it to pass
the discontinuity irrespective of the output of the internal error
estimator).

Kjell
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    mail: Kjell Gustafsson, Department of Computer Science MJH309
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