  Spectral deferred corrections (SDC) is an iterative approach for constructing
higher- order accurate numerical approximations of ordinary differential
equations. SDC starts with an initial approximation of the solution defined at
a set of Gaussian or spectral collocation nodes over a time interval and uses
an iterative application of lower-order time discretizations applied to a
correction equation to improve the solution at these nodes. Each deferred
correction sweep increases the formal order of accuracy of the method up to the
limit inherent in the accuracy defined by the collocation points. In this
paper, we demonstrate that SDC is well suited to recovering from soft
(transient) hardware faults in the data. A strategy where extra correction
iterations are used to recover from soft errors and provide algorithmic
resilience is proposed. Specifically, in this approach the iteration is
continued until the residual (a measure of the error in the approximation) is
small relative to the residual on the first correction iteration and changes
slowly between successive iterations. We demonstrate the effectiveness of this
strategy for both canonical test problems and a comprehen- sive situation
involving a mature scientific application code that solves the reacting
Navier-Stokes equations for combustion research.
