Perform step refactor for Tsit

[ParamThakkar123]

Checklist

• Appropriate tests were added
• Any code changes were done in a way that does not break public API
• All documentation related to code changes were updated
• The new code follows the
  contributor guidelines, in particular the SciML Style Guide and
  COLPRAC.
• Any new documentation only uses public API

Additional context

Add any other context about the problem here.
solves a part of #233

[oscardssmith]

how does the performance compare?

[ChrisRackauckas]

Explicit RK is a bit tougher. It has a lot harder performance-wise. It needs a good understanding of #233 (comment)

[ParamThakkar123]

Okay. I will refer that comment

[ParamThakkar123]

@ChrisRackauckas Just needed your review on this. All the tests that have failed show some sort of precision and dimension mismatch.

[ChrisRackauckas]

I don't understand the point of this PR. As mentioned in the other threads and the comment above, the general tableau for ERK methods is about feature-completeness and correctness of ExplicitRK and subsuming other RKs into that.

[ParamThakkar123]

I don't understand the point of this PR. As mentioned in the other threads and the comment above, the general tableau for ERK methods is about feature-completeness and correctness of ExplicitRK and subsuming other RKs into that.

Actually, all I did here is refactor of perform_step implementations focusing only on the tsit solvers. The Tsit tableau was implemented in the library for this solvers. So I just refactored it that way. Focusing only on this.

[ChrisRackauckas]

Yes, that does not make sense given ExplicitRK exists.

[ParamThakkar123]

Yes, that does not make sense given ExplicitRK exists.

So should I be doing ExplicitRK first and then combining tsit into it ??

[ChrisRackauckas]

ExplicitRK exists and has a Tsit5 tableau already. Its mostly about feature-completeness and performance now.

[ParamThakkar123]

So what should be done further as far as this PR is concerned ?

[ParamThakkar123]

@ChrisRackauckas should I move on with the refactoring of ExplicitRK first ??

[ChrisRackauckas]

No it's already "refactored". It's about improving it and feature completing it. Testing it against the other implementations of RKs and making sure it floating point matches, and making sure default controller values are set appropriately.

[ParamThakkar123]

No it's already "refactored". It's about improving it and feature completing it. Testing it against the other implementations of RKs and making sure it floating point matches, and making sure default controller values are set appropriately.

Got it. Should I work towards feature completing it? What should be the first thing that should be done to start off with that ?

[ChrisRackauckas]

Run Tsit5 and the tableau form of Tsit5 and get the times array to match exactly. I think the controller params are probably the place to start.

[ParamThakkar123]

Run Tsit5 and the tableau form of Tsit5 and get the times array to match exactly. I think the controller params are probably the place to start.

@ChrisRackauckas I ran the Tsit5 and its tableau form on a sample DE as follows :

and the times arrays seem to match exactly

[ChrisRackauckas]

What about with stiffness detection and switching?

[ParamThakkar123]

What about with stiffness detection and switching?

code :

@ChrisRackauckas

[ChrisRackauckas]

I mean build an autoswitch alg that uses the ExplicitRK version, does that match the Tsit5 behavior?