On Tue, Mar 2, 2010 at 11:44 AM, Jed Brown <[email protected]> wrote:
> * At each stage of the implicit system, integrate the explicit system up
> to the current stage using interpolated values of the implicit system.
> If the final abscissa is 1 and the implicit method has full stage
> order, then I think this is nominally of full accuracy
> (i.e. min(implicit_order,explicit order)). This is burying the
> explicit integrator in function evaluation for the implicit system.
> Dana told me that he has actually done this in the past, albeit for
> simpler implicit integrators.
>
This is what we do now.... and we match the implicit and explicit
integration orders. This is really what we'd need to be able to do before I
could use TSGL.
> TSGL is not currently set up to offer the high-order interpolation at
> arbitrary points within the interval, especially before all the stages
> have been solved, but the method can supply these values (I or
> (preferably) the inventors of the method just need to work out the
> details for this operation). I would like to have it anyway for
> integration of continuous adjoints (discrete adjoints don't need
> interpolation).
Bummer... if you have a trial implementation at some point that you want me
to try out... I'm all game!
Derek
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