Multirate: add implicit MRI-GARK-ESDIRK46a (order 4) (#961)#3886
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Adds MRI-GARK-ESDIRK46a (Sandu 2019), completing the implicit MRI-GARK family alongside IRK21a (#3811) and ESDIRK34a (#3812), closing #961.
While implementing it I found that the implicit MRI-GARK path ignored the tableau embedding and always estimated the error as
u - z[s]. For ESDIRK46a this is always zero because the method is stiffly accurate, causing every step to be accepted. This PR uses the embedding row when present, matching the existing explicit implementation, while preserving the previous behavior for methods without an embedding.Also replaces the repeated
Union{MRIGARKIRK21a, MRIGARKESDIRK34a}with the existingMRIGARKImplicitAlgalias.Validation:
Bumps OrdinaryDiffEqMultirate to v2.7.0. Not re-exported from the umbrella package, matching the existing multirate methods.
AI Disclosure:
Claude assisted with this work.