ESDIRK* methods listed as IMEX schemes

[MarcoArtiano]

According to the docs https://docs.sciml.ai/DiffEqDocs/stable/api/ordinarydiffeq/implicit/SDIRK/#IMEX-SDIRK the ESDIRK* methods are listed as IMEX schemes. However, they do not account for ODE split problems. In this sense, the documentation seems confusing.

[ChrisRackauckas]

But for example KenCarp4 does act differently on SplitODEProblem? It has a separate tableau for that?

[MarcoArtiano]

But for example KenCarp4 does act differently on SplitODEProblem? It has a separate tableau for that?

Yes, KenCarp* methods seem to act correctly in case of a SplitODEProblem. See for example: trixi-framework/Trixi.jl#2518 (comment)