 
Summary: MATHEMATICS OF COMPUTATION
Volume 00, Number 0, Pages 000000
S 00255718(XX)00000
IMPLICITEXPLICIT MULTISTEP METHODS
FOR NONLINEAR PARABOLIC EQUATIONS
GEORGIOS AKRIVIS
Abstract. Implicitexplicit 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 timeindependent, selfadjoint 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 allowing part
of it to be timedependent or nonselfadjoint. We establish optimal order a
priori error estimates.
1. Introduction
Let T > 0, u0
H, and consider the initial value problem of seeking u : [0, T]
D(A) satisfying
(1.1)
{
u
