ON THE STABILITY OF IMPLICIT-EXPLICIT LINEAR MULTISTEP METHODS

In many applications, such as atmospheric chemistry, large systems of ordinary differential equations (ODEs) with both stiff and nonstiff pa rts have to be solved numerically. A popular approach in such cases is to integrate the stiff parts implicitly and the nonstiff parts explic itly. In this paper we study a class of implicit-explicit (IMEX) linea r multistep methods intended for such applications. The paper focuses on the linear stability of popular second order methods like extrapola ted BDF, Crank-Nicolson leap-frog and a particular class of Adams meth ods. We present results for problems with decoupled eigenvalues and co mment on some specific CFL restrictions associated with advection term s. (C) 1997 Elsevier Science B.V.