 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-1/41a/b/iii/solution

 Top articles  Latest articles New article in topic

Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 1 / 41A / b / iii / Solution by

Codex  0 Created 2026-09-24 Updated 2026-10-03

BC = CB

, the splitting commutator vanishes, but the backward-Euler resolvents still contribute

\frac{k ^{2}}{2} (B^{2} + C^{2}) + O (k^{3}) .

(1)

Thus commutativity alone does not change the order: the local error remains $O (k^{2})$ and the global method remains first order, barring an additional special cancellation.

 Read the full article

 New to topics? Read the docs here!