  Spectral deferred correction (SDC) methods are an attractive approach to
iteratively computing collocation solutions to an ODE by performing so-called
sweeps with a low-order time stepping method. SDC allows to easily construct
high order split methods where e.g. stiff terms of the ODE are treated
implicitly. This requires the solution to full accuracy of multiple linear
systems of equations during each sweep, e.g. with a multigrid method. In this
paper, we present an inexact variant of SDC, where each solve of a linear
system is replaced by a single multigrid V-cycle and thus significantly reduces
the cost for each sweep. For the investigated examples, this strategy results
only in a small increase of the number of required sweeps and we demonstrate
that "inexact spectral deferred corrections" can provide a dramatic reduction
of the overall number of multigrid V-cycles required to complete an SDC time
step.
