Extend WorkPrecisionSet to DDE problems

[devmotion]

I just noticed that currently no DDE benchmarks can be performed since no WorkPrecisionSet can be created for DDE problems. It seems this issue is caused by the restructuring in 8de789c#diff-826047b6175ac9aca7e1958367322880.

[ChrisRackauckas]

Would a better way of handling this be to make both it and AbstractDAEProblem subtypes of AbstractODEProblem? DAEs should get the same treatment here.

[coveralls]

Coverage remained the same at 95.984% when pulling a79e9d7 on devmotion:fix_dde into 31dbb34 on JuliaDiffEq:master.

[codecov]

Codecov Report

Merging #7 into master will not change coverage.
The diff coverage is n/a.

@@           Coverage Diff           @@
##           master       #7   +/-   ##
=======================================
  Coverage   95.98%   95.98%           
=======================================
  Files           7        7           
  Lines        7172     7172           
=======================================
  Hits         6884     6884           
  Misses        288      288

Impacted Files	Coverage Δ
src/benchmark.jl	83.68% <ø> (ø)	⬆️

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[devmotion]

I like your idea. The only problem I see is that this type structure might not go well with SciML/DelayDiffEq.jl#29. Another alternative would be to introduce a new abstract supertype for all these problems, but I'm not completely sure about the (dis)advantages of this approach.

[ChrisRackauckas]

I am thinking that everything goes under AbstractODEProblem or AbstractRODEProblem, keeping stochastic separate from deterministic since they are treated very differently. OrdinaryDiffEq.jl should start handling DAEs soon enough while StochasticDiffEq.jl already patches in so that way it can handle both RODEs and SDEs, so we're already moving in the direction of clumping these things together. DelayDiffEq.jl should probably dispatch on that level to get the correct implementation when the time comes.

[devmotion]

Yeah, separating stochastic and deterministic problems is the best approach, I guess. I'm just slightly confused how AbstractDDEProblem would fit in that type hierarchy, considering that it could be both stochastic and deterministic. Wouldn't this require two different subtypes such as AbstractDDEProblem and AbstractSDDEProblem? But maybe it's not necessary to discuss that now... Anyway, I guess I can close this issue since we should rather change the current type hierarchy?

[ChrisRackauckas]

Just add AbstractDAEProblem to the deterministic dispatches here and we can merge. We can discuss better use of the type hierarchy in another issue.

[ChrisRackauckas]

Merge when tests pass