Solution (source code)

= Solution

The five-point expression satisfies $\Gamma_5f=h^2\Delta f+O(h^4)$. Therefore the modified right side is $h^2f+h^4\Delta f/12+O(h^6)$, cancelling the leading residual from part (a) and leaving the same $O(h^6)$ local error as in part (c).