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

[nlin@nlin.net]

> actually i'm not sure what a higher order time stepping scheme
> will look like in this case. i'd have to sit down and read some
> papers and write some equations. it's not a problem i have
> considered yet.

I found a doctoral dissertation which appears extremely relevant, where
the author extends Stewart's time stepping scheme to use a trapezoidal
method for the ODE integration, and says that basically any higher order
integrator can be used. He provides algorithm outlines and detailed
formulas.  Equation 3.24 on p. 95 and the algorithm outline starting
on the bottom of p. 98 are noteworthy. However the whole thing seems to
be based on an NCP formulation, not an LCP formulation, so it looks like
it would require the use of NCP solution methods to incorporate this
into ODE.

http://www.mts.jhu.edu/~jimt2/dissertation.pdf

I wrote to the author and asked if his simulation code (which runs under
Linux) is available, and will report back to the list.

-Norman