implement ROW (or regular Rosenbrock) semi-implicit integration.

[kaschau]

Implement a Rosenbrock type method for chemistry integration.

Advantages: Single step, non iterative. "Looks like" RK schemes.

Disadvantages (/ really advantages) : Requires jacobian.

See

https://encyclopediaofmath.org/wiki/Rosenbrock_methods
http://www.hysafe.org/science/eAcademy/docs/ACMTransactionsOnMathematicalSoftware_v8_p93to113.pdf
https://www.sciencedirect.com/science/article/pii/S0377042715001569
https://www.epfl.ch/labs/anchp/wp-content/uploads/2018/05/part2-1.pdf

Then further implemented with the simpler operator splitting detailed in #32

Could be a massive speedup, and would be done in Kokkos spaces rather than on the python side.

[kaschau]

Good paper on state function choice
https://www.sciencedirect.com/science/article/pii/S0010218018301275#bib0002

[kaschau]

About jacobians:

Full analytical jacobian with constant pressure assumption
https://arxiv.org/pdf/1605.03262.pdf

Full and approximate analytical jacobians with constant volume assumption
https://pubs.acs.org/doi/pdf/10.1021/ef300747n

Seems ROW may be a good choice if we can find a simpler, but accurate enough approx to the Jacobian, given that ROW only need jacobian approximations (in contrast to typical Rosenbracks which may be very sensitive to Jacobians)

[kaschau]

Some papers on GPU chemistry

https://www.sciencedirect.com/science/article/pii/S0010465512003463
https://www.sciencedirect.com/science/article/pii/S0010218014003459
https://www.sciencedirect.com/science/article/abs/pii/S0010218017300354