Herman Sletmoen

I think this could also be a great way to offload some information from `show()`. The display of `sys` could prioritize the numerical aspect which is convenient for interactive use...

At least "Basic Blocks" libraries and `Interpolation`, `ParametrizedInterpolation`, `SampledData`, ... components sound domain-independent and generically useful to me and makes sense to have in a standard library. Electrical/magnetic/mechanical/thermal/... components sound...

Is the automatic preconditioner in the works? It would be really nice.

Would it be easy to fix that? Where would I have to look?

What is the state of exploiting ODE linearity in stiff solvers now in 2025? I am very interested in getting this to work.

> Newton's method actually has a guarantee that if f is linear then it will step to the root in 1 step regardless of the initial guess. Ok, that's great,...

Thank you, I will look out for #2727. For adaptive: the example above has `250+117` (attempted) steps, but `1264` nonlinear solver iterations. Should not 1 attempted step require 1 nonlinear...

> If you force new jac on each step then it should be different Like so? Here for Implicit Euler, TRBDF2 and KenCarp4. Are they still not doing many more...

Yes exactly, but why 144 nonlinear solves on 12 steps? I get there is a factor 6x since KenCarp4 has 6 stages, but where is the additional factor 2x from?

`nsolve` is incremented [inside each Newton iteration](https://github.com/SciML/OrdinaryDiffEq.jl/blob/4abda1b6b4b8985e2bd3747fce11e5983d121fc6/lib/OrdinaryDiffEqNonlinearSolve/src/newton.jl#L203), which makes sense. It is also incremented [inside the ODE step](https://github.com/SciML/OrdinaryDiffEq.jl/blob/4abda1b6b4b8985e2bd3747fce11e5983d121fc6/lib/OrdinaryDiffEqSDIRK/src/kencarp_kvaerno_perform_step.jl#L1122), but is this superfluous? And is [this `linres`](https://github.com/SciML/OrdinaryDiffEq.jl/blob/4abda1b6b4b8985e2bd3747fce11e5983d121fc6/lib/OrdinaryDiffEqSDIRK/src/kencarp_kvaerno_perform_step.jl#L129C1-L130C34) dead code?