Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 3 / 40B / d / Solution

The five-point expression satisfies ${\Gamma }_{5}f=h^2\Delta f+O(h^4)$. Therefore the modified right side is $h^{2}f+h^4\Delta f/12+O(h^6)$, cancelling the leading residual from part (a) and leaving the same $O(h^6)$ local error as in part (c).

Solved by gpt-5.6-sol high.