Review of the past two weeks

In the last two weeks, the main work still focuses on the refactorization and external solver API implementation, some progress can be summarized as follows:

Matrices and vector indices refactoring still have some left which are quite tricky to continue, the main refactoring is located in the subroutine of collocation equations setup, e.g. the global BVP matrices, the matrices represent solutions and their derivative, which is the most important part of the solver.
Continue previous work on the implementation of extension from ODEInterface.jl, mainly about interfacing the COLNEW solver into BoundaryValueDiffEq.jl, detailed progress can be checked here: COLNEW supports multi-points BVP for now there are testing errors about MultipleShooting methods, but it will be addressed soon.
The initial version of COLDAE in ODEInterface.jl, it would be great to have COLDAE interface in ODEInterface.jl, which would provide us more intuitive and easy-to-use API to compare and benchmark our implementation, detailed progress can be checked here: Add COLDAE solver.

More TODOs:

Continue the current pull request and finish these features as soon as possible.
Refactor the nonlinear iteration process and utilize the init-cache-solve-cache process in MIRK solvers.
Continue to refactor the solver, especially the collocation equations setting up part.
Try the implemented solver on different examples and see if there are any improvements we need to complete.