Summary: MATHEMATICS OF COMPUTATION
Volume 00, Number 0, Pages 000000
IMPLICITEXPLICIT MULTISTEP METHODS
FOR NONLINEAR PARABOLIC EQUATIONS
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 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 allowing part
of it to be time-dependent or nonself-adjoint. We establish optimal order a
priori error estimates.
Let T > 0, u0
H, and consider the initial value problem of seeking u : [0, T]