`t_eval` of `CyRK` behaves different to `solve_ivp` about cyrk

[jrenaud90]

Hi, @fvollmer! Yes this is a missing feature of CyRK. It would not be too difficult to implement: solve_ivp uses a dense output which estimates the value of your problem inbetween solution steps (sorta like a faster, more accurate interpolation).

See here for the main implementation in SciPy and here for the RK specific implementation.

• Update RK constants to include the versions used for dense output.
• For nbrk: Create a python class that largely mimics the dense output class used in SciPy. Add this as an optional return to nbrk_ode.
• For cyrk and CySolver: Create a cython class that does the same. For cyrk_ode this can be an additional output. For CySolver this class could be partially instantiated early on and then stored in the CySolver class as <instance_name>.dense and used like <instance_name>.dense(new_x) -> new_y.

I will mark this as a todo for a future update (PRs are welcome if you or others want to work on this!)

In the mean time feel free to share a simple working example of your code. I would be curious why the interpolation is so severely impacting performance. If you are not using the CySolver approach then that would be a way to greatly improve performance.

Cheers!