For solving hyperbolic systems with stiff sources or relaxation terms, time stepping methods should combine favorable monotonicity properties for shocks and steep solution gradients with good stability properties for stiff terms. In this paper we consider implicit-explicit (IMEX) multistep methods. Suitable methods will be constructed, based on explicit methods with general monotonicity and boundedness properties for hyperbolic equations. Numerical comparisons are made with several implicit-explicit Runge-Kutta methods.
Academic Press Professional, Inc. San Diego, CA, USA
Journal of Computational Physics
Multiscale Dynamics

Hundsdorfer, W, & Ruuth, S.J. (2007). IMEX extensions of linear multistep methods with general monotonicity. Journal of Computational Physics, 225(2), 2016–2042.