Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 341 / 1 / b / Solution

At $h=0$ the first characteristic polynomial isIts roots satisfy the root condition for a multistep method: the only unit-modulus root is the simple root $1$, and the other root has modulus $1/5$. The method is consistent because part a gives positive order. The Dahlquist equivalence theorem, in the form allowed by the question for this derivative-augmented method, therefore proves convergence.