Use Jacobian-free Newton-Krylov for SDIRK time integrators

[DanielDoehring]

I played a bit with https://docs.sciml.ai/DiffEqDocs/stable/tutorials/advanced_ode_example/#Using-Jacobian-Free-Newton-Krylov

[github-actions]

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 96.71%. Comparing base (9b51a54) to head (fcdfd39).

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #2505      +/-   ##
==========================================
+ Coverage   94.88%   96.71%   +1.83%     
==========================================
  Files         512      514       +2     
  Lines       42443    42479      +36     
==========================================
+ Hits        40268    41080     +812     
+ Misses       2175     1399     -776     

Flag	Coverage Δ
unittests	96.71% <100.00%> (+1.83%)	⬆️

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[JoshuaLampert]

Finally, downgrade tests run 🥳 . So now they only need to pass.

[DanielDoehring]

@jlchan I selected you as reviewer since I changed a typo in one of the existing elixirs :)