$R=$

Discretization method

Preserves Hamiltonian structure?

$\left[I+hA\right]$

forward Euler

No

${\left[I-hA\right]}^{-1}$

backward Euler

No

${\left[I-\frac{1}{2}hA\right]}^{-1}\left[I+\frac{1}{2}hA\right]$

Tustin

Yes

$e^{Ah}$

Pole zero matching

Yes

$\Phi \left(k+1,k\right)=e^{Ah}$

Zero-order hold

Yes