Iterative Methods for the Temporal Integration of PDEs

Abstract
I will present a class of iterative temporal integration methods and
discuss the implications of using iterative methods for the temporal
integration of PDEs. The iterative methods are based on a spectral
deferred correction strategy, and unlike Runge-Kutta or
linear-multistep methods, the order of accuracy of the solution is
increased iteratively by solving a series of correction equations.  I
will outline the possible advantages to using iterative methods for
time integration in relation to multi-scale applications, spatially
adaptive mesh refinement, and parallelization in the temporal
direction.