Second-order backward differentiation formula
= Second-order backward differentiation formula
{title2=$3y_{n+2}-4y_{n+1}+y_n=2h f(y_{n+2})$}
= BDF2 method
{c}
{synonym}
= BDF2
{c}
{synonym}
The displayed implicit <linear multistep method> is second order and <A-stable>. It is the $\alpha=4/3$ member of the <trapezoidal-BDF two-step family>, whose order and boundary-locus proof establish both properties. Its derivative formula uses three equally spaced values; changing the steps requires different coefficients.