Add precompilation stage

[xtalax]

Provides a greater than 3x speedup in first run discretization times, at the cost of 6x precompilation time

fixes #293

[ai-maintainer]

AI-Maintainer Review for PR - Add precompilation stage

Title and Description ❌

Title is clear but description is missing

The title of the pull request is clear and indicates the purpose of the changes. However, the description is missing. It would be beneficial to include a description that provides more context about the changes, such as the motivation behind adding the precompilation stage and how it improves the project.

Scope of Changes ✅

Changes are narrowly focused

The changes in this pull request are narrowly focused on adding a precompilation stage. There are no other changes or modifications in the diff, indicating that the author is specifically addressing the addition of the precompilation functionality.

Testing ❌

No information about testing

The description does not provide any information about how the changes were tested. It would be helpful for the author to include information about the testing process, such as the specific test cases used or any additional steps taken to ensure the correctness and functionality of the added precompilation stage.

Code Changes ✅

Code changes are appropriate

The code changes appear to be appropriate for the addition of a precompilation stage. The author has added the `PrecompileTools` package to the project and used it in the `MethodOfLines.jl` file. A new file `precompile.jl` has also been added which contains the precompilation logic.

Suggested Changes

• Please add a description to the pull request that provides more context about the changes, such as the motivation behind adding the precompilation stage and how it improves the project.
• Please provide information about how the changes were tested, such as the specific test cases used or any additional steps taken to ensure the correctness and functionality of the added precompilation stage.

Reviewed with AI Maintainer

[codecov]

Codecov Report

Merging #300 (da7fc25) into master (c360747) will increase coverage by 0.74%.
The diff coverage is 95.23%.

@@            Coverage Diff             @@
##           master     #300      +/-   ##
==========================================
+ Coverage   81.56%   82.31%   +0.74%     
==========================================
  Files          36       37       +1     
  Lines        1660     1702      +42     
==========================================
+ Hits         1354     1401      +47     
+ Misses        306      301       -5     

Files Changed	Coverage Δ
src/MethodOfLines.jl	100.00% <ø> (ø)
src/precompile.jl	95.23% <95.23%> (ø)

... and 2 files with indirect coverage changes

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