The basics of DiscreteSystem exists now, but the little details around it need to be finished.

there need more results of predictions for a system of PDE and compare with reliable results.

http://eqworld.ipmnet.ru/en/solutions/syspde.htm

castro.change_max = 1.0 means that the timestep can only ever stay the same or decrease relative to its initial value. I think we should disallow this value, I have a hard time imagining a use case for this (if you want a fixed timestep, use fixed_dt, and if you want a timestep cap but still allow the timestep to decrease, use max_dt). It causes problems with the retry functionality.