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

The centered spatial second difference has error $O(\Delta x^2)$. The symmetric compositionis 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