Abstract

An implicit-explicit multistep method based on the backward difference formulae (BDF) is proposed for time discretization of parabolic equations with a non-selfadjoint operator. Implicit and explicit schemes are used for the self-adjoint and anti-selfadjoint parts of the operator, respectively. For a $k$-step method, some correction terms are added to the starting $k-1$ steps to maintain $k$th-order convergence without imposing further compatibility conditions at the initial time. Long-time $k$th-order convergence for the numerical method is proved under the assumptions that the operator is coercive and the non-selfadjoint part is low order. Such an operator often appears in practical computation (such as the Stokes--Darcy system), but may violate the standard sectorial angle condition used in the literature for analysis of BDF.