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Christopher Rackauckas
@ChrisRackauckas
With automatic differentiation... that's interesting. I'd like to test that out vs other methods.
Paweł Biernat
@pwl
I tested it with a hyperbolic PDE that I work on and it worked as quick as RK
Christopher Rackauckas
@ChrisRackauckas
I thought of using symbolic differentiation before with Taylor methods.
Paweł Biernat
@pwl
at least the same order of magnitude
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
Christopher Rackauckas
@ChrisRackauckas
Probably scales better than extrapolation.
Paweł Biernat
@pwl
but this is a niche application
Christopher Rackauckas
@ChrisRackauckas
Well you'd need to go to other numbers to avoid weird truncation error problems at that point.
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.
Mauro
@mauro3
@PerezHz looks into taylor methods in his PhD with Benet & Sanders: https://github.com/JuliaLang/ODE.jl/issues/91#issue-139761284
Christopher Rackauckas
@ChrisRackauckas
But @pwl said the package is no longer available?
Paweł Biernat
@pwl
unfortunately the package disappeared
I still have a hard copy on my hd
Christopher Rackauckas
@ChrisRackauckas
Please share :smile:
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.
Paweł Biernat
@pwl
I don't know how @PerezHz would feel about it, maybe you should write him first?
Christopher Rackauckas
@ChrisRackauckas
Okay, I'll email him.
Thanks for the heads up on this
Paweł Biernat
@pwl
if you won't be able to reach him you can try to write @lbenet, he will know what the status of the package is
I think he is his advisor, but I'm not so sure about it now:-)
Jorge Pérez
@PerezHz
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
Christopher Rackauckas
@ChrisRackauckas
Okay cool!
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.
Paweł Biernat
@pwl
Are there any plans to release the interval arithmetic ODE solver? I saw something like that on @lbenet presentation.
Jorge Pérez
@PerezHz
Sure Chris, we'll let you know!
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
Christopher Rackauckas
@ChrisRackauckas
Are you going to be using ArbReals? I know dpsanders is in on that project.
Jorge Pérez
@PerezHz
AFAIK, we'll be using @dpsanders ValidatedNumerics.jl
Christopher Rackauckas
@ChrisRackauckas
I see
This application would be perfect for ArbReals though.
Though Interval{Float64} would be faster for small calculations, Interval{BigFloat} would do better than ArbReals if you need 500+ bits of accuracy.
But in the middle, 64-~500 bits, ArbReals is the way to go.
I kow Sanders and Benet have been on the emails with Jeffrey Sarnoff on ArbFloats/ArbReals, so I wonder if that's why.
Felix Henneke
@fhenneke
I might be mistaken, but should the name fehlberg in runge-kutta-fehlberg not be spelled with an E instead of a U?
Christopher Rackauckas
@ChrisRackauckas
Yes.
Where's do I have the error?
Felix Henneke
@fhenneke
everywhere? e.g. on the first page of the documentation and in the ode_tableaus.jl in the source code
Christopher Rackauckas
@ChrisRackauckas
oh...
:worried:
Thanks for letting me know!
Felix Henneke
@fhenneke
btw: keep up the good work! :)
Christopher Rackauckas
@ChrisRackauckas
Thanks!
Romain Veltz
@rveltz
HI,
I tried the simple code
'using DifferentialEquations

function vanDerPolExample(u₀=[0,sqrt(3)])
f1(u,t) = (1-u[2].^2)*u[1] - u[2]
f2(u,t) = u[1]
f(u,t) = [f1(u,t);f2(u,t)]
return(ODEProblem(f,u₀))
end
prob = vanDerPolExample()
Δt = 1//2^(4) #The initial timestepping size. It will automatically assigned if not given.
tspan = [0,20] # The timespan. This is the default if not given.
sol = solve(prob::ODEProblem,tspan,Δt=Δt,alg=:RK4)'

but it gives the error (line 12 is the solve):

ERROR: LoadError: BoundsError
in getindex at ./number.jl:21 [inlined]
in (::#f1#10)(::Rational{Int64}, ::Array{Float64,1}) at /Users/rveltz/Downloads/ode.jl:4
in (::#f#12{#f1#10,#f2#11})(::Rational{Int64}, ::Array{Float64,1}) at /Users/rveltz/Downloads/ode.jl:6
in (::DifferentialEquations.##500#507{DifferentialEquations.ODEProblem{Array{Float64,1},Float64}})(::Rational{Int64}, ::Array{Float64,1}, ::Array{Float64,1}) at /Users/rveltz/.julia/v0.5/DifferentialEquations/src/ode/ode_solve.jl:79
in ode_solve(::DifferentialEquations.ODEIntegrator{:RK4,Array{Float64,1},Float64,2,Rational{Int64}}) at /Users/rveltz/.julia/v0.5/DifferentialEquations/src/ode/ode_integrators.jl:376
in #solve#499(::Array{Any,1}, ::Function, ::DifferentialEquations.ODEProblem{Array{Float64,1},Float64}, ::Array{Int64,1}) at /Users/rveltz/.julia/v0.5/DifferentialEquations/src/ode/ode_solve.jl:134
in (::DifferentialEquations.#kw##solve)(::Array{Any,1}, ::DifferentialEquations.#solve, ::DifferentialEquations.ODEProblem{Array{Float64,1},Float64}, ::Array{Int64,1}) at ./<missing>:0
in include_from_node1(::String) at ./loading.jl:426
in include_from_node1(::String) at /Applications/Julia-0.5.app/Contents/Resources/julia/lib/julia/sys.dylib:?
while loading /Users/rveltz/Downloads/ode.jl, in expression starting on line 12

Do you have any idea?

Thank you,



Christopher Rackauckas
@ChrisRackauckas
Are you on master? Then the API changed to (t,u) and (t,u,du) to match ODE.jl, ODEInterface.jl, and Sundials.jl. IF you're not on master, than it's okay.