Past exam of the mathematics course of the University of Cambridge / 2021 / ib / Paper 1 / 17B / i / Solution

The local truncation error is the error made by one numerical step started from the exact solution:A one-step method has local order $p+1$ when ${\tau }_{n+1}=O(h^{p+1})$ uniformly for $t_n$ in each fixed bounded time interval.