Format & Comment custom integrators

[DanielDoehring]

No description provided.

[github-actions]

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 with its PR number.

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.
• If the PR intent is to improve performance, before/after time measurements are posted in the PR.

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 ❤️ by the Trixi.jl community.

[JoshuaLampert]

Looks mostly good to me. I have only one small formatting question.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 96.37%. Comparing base (f09a707) to head (b2aaf75).

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #2218   +/-   ##
=======================================
  Coverage   96.37%   96.37%           
=======================================
  Files         486      486           
  Lines       39186    39186           
=======================================
  Hits        37764    37764           
  Misses       1422     1422           

Flag	Coverage Δ
unittests	96.37% <100.00%> (ø)

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[JoshuaLampert]

LGTM