Yes, it’s a weak point of SciML. But we have a pretty grand plan for fixing it. Most BVP solvers specialize too much on ODE 2-point boundary problems, or lose any specialization. By mixing LinearSolve.jl, NonlinearSolve.jl, SparseDiffTools.jl, and ModelingToolkit.jl tearing you can generalize the specialization to a much larger class of problems since you then no longer require just a banded matrix structure (but can always automatically recover a banded matrix), which would make a much better MIRK method. Of course, that is a bit hard to see with the naked eye, but that’s how it’s progressing. We need some more development in those other tools before piecing it all together though, but would be interested to have any help possible.
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