Implicit–explicit multistep methods for nonlinear parabolic equations

Abstract

Implicit–explicit multistep methods for nonlinear parabolic equa- tions were recently analyzed in [2, 3, 1]. In these papers the linear operator of the equation is assumed to be time-independent, self-adjoint and positive definite; then, the linear part is discretized implicitly and the remaining part explicitly. Here we slightly relax the hypotheses on the linear operator by al- lowing part of it to be time-dependent or nonself-adjoint. We establish optimal order a priori error estimates.