@pwl This is a good SE post for explaining the difference between the major groups., and here is another reference for the differences . We might think about writing a wrapper to PFASST. Actually I think it we wrap enough of them or put enough of these algorithms under the same roof we might be able to get a review article out of it.
In the end I am looking to try a few of them since I am interesting in which ones may be useful for stochastic differential equations.
But I don't really think that any program puts all of these together already, so this is something to be done.
While I'm at it, the other ODE methods I am looking into implementing are super high order RKs.
Let me know if you plan on implementing any of these so we don't double up!
the fun thing with this method is that you can prescribe an error much lower then the machine epsilon
like reltol 1e-30 with
Float64
But a battle between high-order extrapolation, RK16, and 16th order Taylor series via automatic differentiation.
I'd want to try that out just for fun.
People in astrodynamics may find that useful.
@PerezHz looks into taylor methods in his PhD with Benet & Sanders: https://github.com/JuliaLang/ODE.jl/issues/91#issue-139761284
I still have a hard copy on my hd
It will have to be updated for sure.
I know ForwardDiff no longer exports the derivative functions, so someone will have to go in and change those kinds of things.
Thanks for the heads up on this
I think he is his advisor, but I'm not so sure about it now:-)
Hi everyone! @ChrisRackauckas thanks for contacting us, glad to know you're interested in what we've been working on! :smile: Yes, we did take it down, we're re-organizing it (it's pretty much mixed with some celestial mechanics stuff) and planning to re-upload the generic parts of the code
I am currently wrapping a bunch of packages into DifferentialEquations.jl, and would like to have that as one of the options to choose from.
Just let me know when you got something you want to show.
Yes @pwl there are plans, we're still working on it; the thing is, the leap towards interval arithmetics is non-trivial enough, @lbenet can give you more details about that