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
$$
O(\Delta t^2+\Delta x^2).
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 341 / 5 / b / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/iii/paper-341/5/b/solution