I am trying to test some algebraic theory using many different Runge-Kutta schemes, with varying order, number of stages, stability, etc. Does anybody have a reference with a coherent list of lots of established RK schemes and their stability functions? I have pieced together a good number from various books and literature, but an encyclopedia of sorts would be very useful.
Ben
John Butcher developed the stability theory for Runge-Kutta methods and suspect his book(s) have the Butcher tableau's for many orders and cases.
http://www.uotechnology.edu.iq/dep-production/branch1_files/Numerical%20Methods%20for%20Ordinary%20Differential%20Equations%20-%20J.%20C.%20Butcher.pdf
And it does not require Dr. Dodd's pills like certain matrices.
Thanks for the list of references! Steve, I have Butcher's third edition and have found the conceptual discussion to be very in depth, but, in quantity, there are not as many specific tableauxs and stability functions as I am looking for. Looks like I may have to pull form lots of sources, starting with Carlos' list.
This is a very good overview that includes many DIRK methods, including their stability and origin:
https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20160005923.pdf
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