Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 341 / Section A / 1 / a

Substitute the exact solution and expand every value about $t_n$. The coefficient of $h^q{y}^{(q)}(t_n)$ in the defect is zero for $q=0,\dots ,p$ exactly whenThese are the order conditions for a linear multistep method, specialized to the two nonzero derivative coefficients. The first failed identity determines the leading local truncation error.