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

[nlin@nlin.net]

> Is it possible to write a simple way document (like a draft) in order to
> provide just the necessary requirement to implement new integrators ?

I'd be interested in seeing this information as well, but as far as I
understand, ODE uses a time-stepping formulation for the rigid body problem,
meaning that the specific integrator used is tied in tightly with the
entire solution scheme, meaning you can't swap out integrators easily.

But, a question to Russ: in "Time stepping methods and the mathematics of
rigid body dynamics" (Stewart, 199x, ftp.math.uiowa.edu/pub/comp_math_rep/report-130.ps.Z),
on p. 30, "Hybrid schemes: DAE's and time stepping", the author states:
"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."

As I understand it ODE does not currently use a hybrid method, but
exclusively uses a partially implicit Euler time stepping method, right?
How difficult would it be to use a hybrid scheme, where the DAE part allows
a user-defined integrator? You mentioned in the ODE docs eventually allowing
other integrators - is this what you had in mind?

-Norman