In many applications, large systems of ordinary differential equations (ODEs) have to be solved numerically that have both stiff and nonstiff parts. A popular approach in such cases is to integrate the stiff parts implicitly and the nonstiff parts explicitly. In this paper we study a class of implicit-explicit (IMEX) linear multistep methods intended for such applications. The paper focuses on the linear stability of popular second order methods like extrapolated BDF, Crank-Nicolson Leap-Frog and a particular class of Adams methods. We present results for problems with decoupled eigenvalues and comment on some specific CFL restrictions associated with advection terms.

Multistep, Runge-Kutta and extrapolation methods (msc 65L06), Stability and convergence of numerical methods (msc 65M12), Method of lines (msc 65M20)
Department of Numerical Mathematics [NM]
Discretization of evoluation problems

Frank, J.E, Hundsdorfer, W, & Verwer, J.G. (1996). Stability of implicit-explicit linear multistep methods. Department of Numerical Mathematics [NM]. CWI.