Solution
= Solution
The centered spatial second difference has error $O(\Delta x^2)$. The symmetric composition
$$
e^{-i(\Delta t/2)T_h}
e^{-i\Delta t V_h}
e^{-i(\Delta t/2)T_h}
$$
is <Strang splitting>, so its local splitting error is $O(\Delta t^3)$ and its global time order is two. Because both semidiscrete subproblems are solved exactly, the total global error is
$$
O(\Delta t^2+\Delta x^2).
$$