Fully implicit, linearly implicit and implicit-explicit backward difference formulae for quasi-linear parabolic equations

摘要

Quasi-linear parabolic equations are discretised in time by fully implicit backward difference formulae (BDF) as well as by implicit-explicit and linearly implicit BDF methods up to order five. Under appropriate stability conditions for the various methods considered, we establish optimal order a priori error bounds by energy estimates, which become applicable via the Nevanlinna-Odeh multiplier technique.