A0-contractivity of the variable-step BDF's of order less than four

We construct a polyhedral norm in which the fixed-step backward differentiation formulas of order one to three are contractive when applied to any differential equation of the formy=(t)y, (t) 0 (i.e. A₀-contractive). The result also holds for non-uniform step-sequences if combined with certain restrictions on the stepwise order-selection.