Backward difference formulae: New multipliers and stability properties for parabolic equations

Source abstract

We determine new, more favorable, and in a sense optimal, multipliers for the three- and five-step backward difference formula (BDF) methods. We apply the new multipliers to establish stability of these methods as well as of their implicit–explicit counterparts for parabolic equations by energy techniques, under milder conditions than the ones recently imposed in [1, 4].