  In this paper we present two strategies to enable "parallelization across the
method" for spectral deferred corrections (SDC). Using standard low-order
time-stepping methods in an iterative fashion, SDC can be seen as
preconditioned Picard iteration for the collocation problem. Typically, a
serial Gauss-Seidel-like preconditioner is used, computing updates for each
collocation node one by one. The goal of this paper is to show how this process
can be parallelized, so that all collocation nodes are updated simultaneously.
The first strategy aims at finding parallel preconditioners for the Picard
iteration and we test three choices using four different test problems. For the
second strategy we diagonalize the quadrature matrix of the collocation problem
directly. In order to integrate non-linear problems we employ simplified and
inexact Newton methods. Here, we estimate the speed of convergence depending on
the time-step size and verify our results using a non-linear diffusion problem.
