The second-order backward differentiation formula is unconditionally zero-stable (Q1119362)

It is well-known that the second order backward differential formula (BDF) is useful for stiff ordinary differential equations and partial differential equations. The authors show that the variable coefficient BDF of order two is \({\mathcal O}\)-stable regardless of the variation of the step-size. They also prove that the fixed coefficient BDF is only conditionally \({\mathcal O}\)-stable.