Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 341 / 1 / a / Solution

Along an exact autonomous-ODE solution, $f(y)=y^{\prime }$ andMove every term to the left and substitute the Taylor expansions about $t_n$. The coefficients of $h^j{y}^{(j)}(t_n)$ vanish for $0\le j\le 4$, while the first nonzero coefficient isThus the local defect is $O(h^5)$. At $h=0$ the first characteristic polynomial iswhich satisfies the root condition for a multistep method. The method is therefore zero-stable and has