[ODE] Other integrators (was: ODE implementors guide)

[nlin@nlin.net]

> > "The time stepping methods presented here are partially implicit
> > Euler methods ... So, ti is probably best to combine DAE methods and
> > time stepping methods; when the DAE method fails, use a timestepping
> > method with small step-size h>0 to get past the impulsive part of the
> > solution, and then re-start the DAE method."
> 
> i don't recall what this paper is about, but i think the point is that
> more "traditional" DAE solution methods can be taylored to give a
> certain desired level of accuracy, but these methods become
> significantly less accurate (and also potentially a lot less stable)
> when the system encounters impulses (e.g. collisions). implicit
> time stepping methods handle the impulses better.

Also, the paragraph I quoted (which I shortened above) talked about the 
(only) first order accuracy of the particular time stepping scheme explained
by Stewart et. al (which seems to be similar or identical to what ODE
uses), so the gist of the above was "use high-order accurate
non-time-stepping DAE methods for normal system evolution, but switch to
a low-order accurate time-stepping method whenever that 'fails'".

-Norman