Numerical schemes implemented

Question

I couldn't find in the manual an explanation about the O2dT scheme implemented in electrics.cc (line 1211). I guess it is a second order in time discretization

$$ \frac{3\phi^{k+1}-4\phi^k+\phi^{k-1}}{2\Delta t}=\frac{1}{2}F(\phi^{k})+\frac{1}{2}F(\phi^{k+1}) $$

with a Crank- Nicolson -like evaluation of $F(\phi^k)$ and

$$ \phi^{k}:=\bar{M_i}V_m^k\,\,\,\,F(\phi^{k}):=-\left(K_i\bar{M_i}^{-1}\right)\bar{M_i}V_m^k  $$

But I couldn't find confirmation of my guess.

Thank you in advance

Answer 1

Yes, it is a second order time integration scheme. Not as well tested as the explicit and Crank-Nicolson schemes, though.