Time integrator in the paired explicit Runge Kutta scheme: Perk p3 single ext

[warisa-r]

Here is the minimal implementation and some tests added in regard to PERK3

• NLsolve has now been added as a weak dependency

TODO:

• Clean up and recheck #1908 so that mistakes in PERK2 are not repeated
• Try the linear case: It does work
• Try the values in matlab script
• Update the tests: test_uni.jl
• test in structured_1d_dgsem

[github-actions]

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[DanielDoehring]

Great work! I added mostly descriptive comments.

[warisa-r]

I'm taking "Make fixed time step and SaveSolutionCallback as per #1958" off the TODO list since:

The reason being, this alteration is directly tied to that pull request. In particular, many abstract objects are defined in methods_PERK2.jl, and they undergo modifications in #1958 By waiting until the said PR is merged, IMHO would minimize any potential conflicts or inconsistencies.

However, if you'd like me to do it anyway, I can assume that it will be merged and make changes to methods_PERK2.jl so that things can be implemented in methods_PERK3.jl so that SaveSolutionCallback works without StepSizeCallback in PERK3.

[warisa-r]

I'm sorry, but I'm unsure if I understand what you say here. Are you suggesting I wait until #1967 is done then come back to this issue later?

[DanielDoehring]

I'm sorry, but I'm unsure if I understand what you say here. Are you suggesting I wait until #1967 is done then come back to this issue later?

Oh no sorry, I clicked the wrong tab in my browser.
I meant (trixi-framework#1958) which is now merged, so you can proceed bringing in the functionality also here :)

[DanielDoehring]

Okay, final request for changes (I hope)! If you have addressed them we can close this here and you can open up the proper PR to the main repository :)

[warisa-r]

In order to make save_solution work like the second-order integrator, some functions in methods_PERK2.jl needed to be modified. I'll do this in the draft PR I will open in the main branch. Thank you for the feedback! Good luck with JuliaCon :D @DanielDoehring