Adding Pseudo-Symplectic Explicit Runge-Kutta methods

[MarcoArtiano]

Checklist

• Appropriate tests were added
• Any code changes were done in a way that does not break public API
• All documentation related to code changes were updated
• The new code follows the
  contributor guidelines, in particular the SciML Style Guide and
  COLPRAC.
• Any new documentation only uses public API

Additional context

This implements some methods mentioned in #1987

references

 "@article{Aubry1998,
    author = {A. Aubry and P. Chartier},
    journal = {BIT Numer. Math.},
    title =  {Pseudo-symplectic {R}unge-{K}utta methods},
    volume = {38},
    PAGES = {439-461},
    year = {1998},
    },
    https://link.springer.com/article/10.1007/BF02510253

    @article{Capuano2017,
    title = {Explicit {R}unge–{K}utta schemes for incompressible flow with improved energy-conservation properties},
    journal = {J. Comput. Phys.},
    volume = {328},
    pages = {86-94},
    year = {2017},
    issn = {0021-9991},
    doi = {https://doi.org/10.1016/j.jcp.2016.10.040},
    author = {F. Capuano and G. Coppola and L. Rández and L. {de Luca}},}"

I just did the ode_convergence_test locally. Please, let me know if any other tests are required. Thank you!

[ranocha]

Thanks for your contribution!

[ranocha]

Thanks a lot! Did you check whether dense output works nicely, e.g., by plotting some numerical solutions?

[ChrisRackauckas]

What's left here?

[MarcoArtiano]

What's left here?

I added proper testing, everything should be fine right now.

[ranocha]

Thanks!