An enhanced parareal algorithm based on the deferred correction methods for a stiff system

In this study, we consider a variant of the hybrid parareal algorithm based on deferred correction techniques in order to increase the convergence order even for the stiff system. A hybrid parareal scheme introduced by Minion (2011) [20] improves the efficiency of the original parareal by utilizing a Spectral Deferred Correction (SDC) strategy for a fine propagator within the parareal iterations. In this paper, we use Krylov Deferred Correction (KDC) for a fine propagator to solve the stiff system and Differential Algebraic Equations (DAEs) stably. Also we employ a deferred correction technique based on the backward Euler method for a coarse propagator in order to make the global order of accuracy reasonably high while limiting the cost of sequential steps as small as possible. Numerical experiments on the efficiency of our method are promising.