E. M. Constantinescu and A. Sandu, "Achieving Very High Order for Implicit Explicit Time Stepping: Extrapolation Methods," Technical Memorandum ANL/MCS-TM-306, April 2009. [pdf]
In this paper we construct extrapolated implicit-explicit time-stepping methods that allow one to efficiently solve problems with both stiff and nonstiff components. The proposed methods can provide very high order discretizations of ODEs, index-1 DAEs, and PDEs in the method of lines framework. Thesemethods are simple to construct, and easy to implement and parallelize. We establish the existence of perturbed asymptotic expansions of global errors, explain the convergence orders of these methods, and explore their linear stability properties. Numerical results with stiff ODEs, DAEs, and PDEs illustrate the theoretical findings and the potential of these methods to solve multiphysics multiscale problems.