[ODE] plans for higher order integrators?

[Gary R. Van Sickle]

> Can somebody (Russ?) tell me if there are short/mid-term
> plans to make higher-order (e.g. Runge-Kutta 4-5) integrators available
> in future versions?

>From what I understand, it isn't that simple, for two reasons:

1.  ODE uses implicit integration instead of the more common explicit type, to
prevent things from exploding.  The main difference here is:

  Explicit:
    X(t0+h) = X(t0)+h*dX(t0)/dt

  Implicit:
    X(t0+h) = X(t0)+h*dX(t0+h)/dt

As you can see, the implicit method then requires considerable machinations to
get it into a usable "X(t0+h) = FunctionOf(X(t0), h)" form.  As I understand it,
such a transformation is simply not possible above 2nd order.

2.  The constraint solving is part of the formulation being integrated, not a
separated stage.  This makes the transformation above all the more difficult.

I've been wondering if there isn't another way of constraining the energy of the
system other than implicit integration.  But other than some handwaving, I
haven't got much past the wondering stage ;-).

--
Gary R. Van Sickle