Added PDIRK and PRK solvers

[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 #2177

[ChrisRackauckas]

Where are the tests for these ones?

[ParamThakkar123]

Where are the tests for these ones?

I didn't see a separate file of tests for these ones but the tests are there in ode_convergence_tests.jl. The convergence test function for PDIRK44 is present inside Implicit Solver Convergence Tests and tests for KuttaPRK2p5 are present in Explicit Solver Convergence Tests

[ParamThakkar123]

@ChrisRackauckas any changes to be made in the tests for these solvers ??

[ChrisRackauckas]

There is a test failure https://github.com/SciML/OrdinaryDiffEq.jl/actions/runs/10133887447/job/28019521857?pr=2303#step:6:953

[ChrisRackauckas]

@oscardssmith https://github.com/SciML/OrdinaryDiffEq.jl/actions/runs/10157523456/job/28087785439?pr=2303#step:6:658 if we don't find a fix soon we'll need to revert the StaticArray change

[oscardssmith]

investigating now.

[oscardssmith]

From initial inspection, this doesn't seem related to my changes since it is happening in addsteps! which is pretty far away in the code from anything with the jacobians...

[ChrisRackauckas]

It's the ArrayInterface.jl changes.

[oscardssmith]

the ArrayInterface change shouldn't have changed anything here... RecursiveArrayTools depends on StaticArrays unconditionally, and StaticArrays has been loaded, so the extension should still be running...

[oscardssmith]

Ah, the problem is that ArrayInterface.ismutable is a generated function that illegally depends on world age I think.

>121  @generated function ArrayInterface.ismutable(::Type{<:ArrayPartition{T, S}}) where {T, S
 122  }
 123      res = all(ArrayInterface.ismutable, S.parameters)
 124      return :($res)
 125  end

[oscardssmith]

problem found. Partial revert incoming.