  Parallel-across-the method time integration can provide small scale
parallelism when solving initial value problems. Spectral deferred corrections
(SDC) with a diagonal sweeper, which is closely related to iterated Runge-Kutta
methods proposed by Van der Houwen and Sommeijer, can use a number of threads
equal to the number of quadrature nodes in the underlying collocation method.
However, convergence speed, efficiency and stability depends critically on the
used coefficients. Previous approaches have used numerical optimization to find
good parameters. Instead, we propose an ansatz that allows to find optimal
parameters analytically. We show that the resulting parallel SDC methods
provide stability domains and convergence order very similar to those of well
established serial SDC variants. Using a model for computational cost that
assumes 80% efficiency of an implementation of parallel SDC we show that our
variants are competitive with serial SDC, previously published parallel SDC
coefficients as well as Picard iteration, explicit RKM-4 and an implicit
fourth-order diagonally implicit Runge-Kutta method.
