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Agreed. First, we should add mass matrices to the BVProblem specification. It needs a BVPFunction, like the ODEFunciton, etc. to add such Jacobian and other metafunctions. That would get mass_matrix, so then linearly implicit BVP DAEs can be specified. Then yes we need to add that to the MIRK method.
It would be nice, if solving of boundary value problems for implicit or semi-explicit DAEs was supported. Such solvers exist in FORTRAN (COLDAE).
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