Implicit–Explicit Multistep Methods for Nonlinear Convection–Diffusion Equations

We construct and analyze implicit–explicit multistep schemes for nonlinear evolution convection–diffusion partial differential equations. We establish optimal order a priori error estimates. We are particularly interested in the dependence of the stability constants on the ratio between the convection and diffusion coefficients, the so-called Peclet number, and on the diffusion coefficient e itself. In particular, we show that the second order implicit–explicit backward differentiation formula (BDF) admits stability constant independent of the Peclet number.