ENH : BDF-2 implementation

[emvalbuena]

• [ ] Review BDF-2 definition in the manuscript.
• [x] Implement.
• Test:
  • [x] Test for existing BDF-1 solution.
  • [x] Test for BDF-2 solution, use conservation of mass as a validation.

See references:

• integration-seance3.pdf

[emvalbuena]

I am finally implementing this because I have realised how slow it is to produce results due to the small time step I need to take (1e-3) to produce meaningful results.

Reminds me of Steven's words about better algorithms: "Computers have peaked, so we can only reach more detailed solutions with better algorithms".

[emvalbuena]

Not surprisingly, I can now cut by half the number of timesteps and yet obtain a better mass conservation.

Well done!

I am quite happy with this feature, because I consider it is the kind of functionality one might inject since the beginning but it doesn't actually change anything about the Reduced Order Model by itself. Thus, I only implemented it when the number of time steps became a problem.

Let problems show up before you fix them ;)