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We establish optimal order a priori error estimates for implicit-explicit BDFmethods for abstract semilinear parabolic equations with time-dependentoperators in a complex Banach space settings, under a sharp condition on thenon-self-adjointness of the linear operator. Our approach relies on thediscrete maximal parabolic regularity of implicit BDF schemes for autonomouslinear parabolic equations, recently established in [20], and on ideas from[7]. We illustrate the applicability of our results to four initial andboundary value problems, namely two for second order, one for fractional order,and one for fourth order, namely the Cahn-Hilliard, parabolic equations.

Maximum norm analysis of implicit-explicit backward difference formulas for nonlinear parabolic equations