[ODE] Euler vs. Runge-Kutta and adaptive step sizes

[nlin@nlin.net]

> I have not seen this time-stepping scheme extended to higher-order 
> integrators, but I have read a paper by Mihai Anitescu (who I think has 
> done work with Stewart and Trinkle) which extends this time-stepping scheme 
> to an implicit integrator (a linearized version of backward-Euler 
> method).  This is useful for systems with stiff forces -- e.g. stiff spring 
> forces.   With explicit methods, these systems tend to "blow up" much easier.

Do you have a URL or a more detailed reference? This sounds quite interesting.

> For what it is worth, I have also seen Anitescu claim in one of his papers 
> that extending the time-stepping scheme to higher order integrators is 
> "non-trivial".

Heh, gotta love it when the leading researchers claim a problem is
"non-trivial". That's why I was so interested in the sample Linux
source code accompanying the PhD dissertation mentioned in 

> >http://q12.org/pipermail/ode/2002-March/000978.html

which, if I recall correctly, implements a higher-order (trapezoidal?)
time-stepping integration scheme (his work also appears to be "non-trivial").

At the time the author didn't want to release his source code (to me), but
maybe if someone with more name recognition (Russ?) wrote and asked, he
might be more amenable to making his work available for improving ODE in
this regard.

-Norman