I need to implement several RK methods with adaptive timestep.
I am however wasting a lot of time in finding consistently Butcher's tableau AND the expressions to evaluate the solution on dense steps. They seem to be dispersed over several publications, and figuring out if they are consistent is taking up a lot of my time.
I am in particular looking for methods like DP54 and TSI54, with different orders for the interpolant.
Can you suggest some reference/review where to find Butcher's tableau AND dense step expressions?
It would also be great if the reference gave any suggestion for optimal parameters for step control techniques.
Thanks!