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

Table of contents
- Solution b

Solution

The centered spatial second difference has error

O (Δ x^{2})

. The symmetric composition

e^{- i (Δ t /2) T_{h}} e^{- i Δ t V_{h}} e^{- i (Δ t /2) T_{h}}

is Strang splitting, so its local splitting error is

O (Δ t^{3})

and its global time order is two. Because both semidiscrete subproblems are solved exactly, the total global error is

O (Δ t^{2} + Δ x^{2}) .

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