On the stability and error structure of BDF schemes applied to linear parabolic evolution equations

We continue the work of various authors on the stability and error structure of multistep schemes applied to linear evolution equations. BDF schemes are considered, and, as far as reasonable, explicit expressions for all occurring bounds are specified, exploiting prior work on the location of characteristic roots. The 2-step BDF scheme is considered in particular detail, and for problems of sectorial type, an asymptotic error expansion is derived based on damping properties of the scheme.