Maximum Norm Analysis of Implicit–explicit Backward Difference Formulae for Nonlinear Parabolic Equations

We establish optimal order a priori error estimates for implicit– explicit BDF methods for abstract semilinear parabolic equations with timedependent operators in a complex Banach space setting, under a sharp condition on the non-self-adjointness of the linear operator. Our approach relies on the discrete maximal parabolic regularity of implicit BDF schemes for autonomous linear parabolic equations, recently established in [19], and on ideas from [6]. We illustrate the applicability of our results to four initial and boundary value problems, namely two of second order, one of fractional order, and one of fourth order, that is the Cahn–Hilliard, parabolic equations.