Perk p2 single ext

[warisa-r]

Hello,

in this PR which is a continuation of the previous PR of PERK2_single, I tried to make Convex and ECOS weak dependencies of Trixi by adding a file called TrixiConvexECOSExt.

Please let me know if something goes wrong and needs improving!

[github-actions[bot]]

Review checklist

This checklist is meant to assist creators of PRs (to let them know what reviewers will typically look for) and reviewers (to guide them in a structured review process). Items do not need to be checked explicitly for a PR to be eligible for merging.

Purpose and scope

• [ ] The PR has a single goal that is clear from the PR title and/or description.
• [ ] All code changes represent a single set of modifications that logically belong together.
• [ ] No more than 500 lines of code are changed or there is no obvious way to split the PR into multiple PRs.

Code quality

• [ ] The code can be understood easily.
• [ ] Newly introduced names for variables etc. are self-descriptive and consistent with existing naming conventions.
• [ ] There are no redundancies that can be removed by simple modularization/refactoring.
• [ ] There are no leftover debug statements or commented code sections.
• [ ] The code adheres to our conventions and style guide, and to the Julia guidelines.

Documentation

• [ ] New functions and types are documented with a docstring or top-level comment.
• [ ] Relevant publications are referenced in docstrings (see example for formatting).
• [ ] Inline comments are used to document longer or unusual code sections.
• [ ] Comments describe intent ("why?") and not just functionality ("what?").
• [ ] If the PR introduces a significant change or new feature, it is documented in NEWS.md.

Testing

• [ ] The PR passes all tests.
• [ ] New or modified lines of code are covered by tests.
• [ ] New or modified tests run in less then 10 seconds.

Performance

• [ ] There are no type instabilities or memory allocations in performance-critical parts.
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Verification

• [ ] The correctness of the code was verified using appropriate tests.
• [ ] If new equations/methods are added, a convergence test has been run and the results are posted in the PR.

Created with :heart: by the Trixi.jl community.

[ranocha]

@DanielDoehring You can ping me for a final review once you're satisfied.

[codecov[bot]]

Codecov Report

Attention: Patch coverage is 86.66667% with 30 lines in your changes are missing coverage. Please review.

Project coverage is 92.56%. Comparing base (887bab9) to head (7bc1ca3).

Files	Patch %	Lines
...ation/paired_explicit_runge_kutta/methods_PERK2.jl	85.44%	23 Missing :warning:
src/Trixi.jl	0.00%	4 Missing :warning:
ext/TrixiConvexECOSExt.jl	96.23%	2 Missing :warning:
...aired_explicit_runge_kutta/polynomial_optimizer.jl	90.00%	1 Missing :warning:

Additional details and impacted files

```diff @@ Coverage Diff @@ ## main #1908 +/- ## ========================================== - Coverage 96.15% 92.56% -3.58% ========================================== Files 454 457 +3 Lines 36509 36702 +193 ========================================== - Hits 35102 33972 -1130 - Misses 1407 2730 +1323 ``` | [Flag](https://app.codecov.io/gh/trixi-framework/Trixi.jl/pull/1908/flags?src=pr&el=flags&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=trixi-framework) | Coverage Δ | | |---|---|---| | [unittests](https://app.codecov.io/gh/trixi-framework/Trixi.jl/pull/1908/flags?src=pr&el=flag&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=trixi-framework) | `92.56% <86.67%> (-3.58%)` | :arrow_down: | Flags with carried forward coverage won't be shown. [Click here](https://docs.codecov.io/docs/carryforward-flags?utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=trixi-framework#carryforward-flags-in-the-pull-request-comment) to find out more.

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[sloede]

Doing a review today (maybe 60% done)

[sloede]

Both test failures looks real: https://github.com/trixi-framework/Trixi.jl/actions/runs/8950168743/job/24585250457?pr=1908#step:7:2058 https://github.com/trixi-framework/Trixi.jl/actions/runs/8950168743/job/24585251161?pr=1908#step:7:1372

[sloede]

@warisa-r I just noticed that a NEWS.md item is missing. Please go through the review checklist once more and that there's nothing else that was forgotten

[DanielDoehring]

Are we good to go here?