An L-stable Butcher tableau for the SDIRK method of order-4 as derived by Hairer & Wanner is shown below.
The implementation of the SDIRK coefficients now becomes
straight-forward, with the Generalized RK formulation.
As a side note, is the lower-diagonalized method a
semi-implicit method? Or is it semi-explicit? Dr. Butcher’s slides have a
rather humorous take on this subject.
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