Argonne National Laboratory

Extrapolated Implicit-Explicit Time Stepping

TitleExtrapolated Implicit-Explicit Time Stepping
Publication TypeJournal Article
Year of Publication2010
AuthorsConstantinescu, EM, Sandu, A
JournalSIAM J. Sci. Comput.
Date Published01/2010
Other NumbersANL/MCS-P1612A-0409

<p>This paper constructs extrapolated implicit-explicit time stepping methods that allow one to efficiently solve problems with both stiff and nonstiff components. The proposed methods are based on Euler steps and can provide very high order discretizations of ODEs, index-1 DAEs, and PDEs in the method of lines framework. Implicit- explicit schemes based on extrapolation are simple to construct, easy to implement, and straightforward to parallelize. This work establishes the existence of perturbed asymptotic expansions of global errors, explains the convergence orders of these methods, and studies their linear stability properties. Numerical results with stiff ODE, DAE, and PDE test problems confirm the theoretical findings and illustrate the potential of these methods to solve multiphysics multiscale problems.</p>