Spectral deferred correction (SDC) methods are an attractive approach toiteratively computing collocation solutions to an ODE by performing so-calledsweeps with a low-order time stepping method. SDC allows to easily constructhigh order split methods where e.g. stiff terms of the ODE are treatedimplicitly. This requires the solution to full accuracy of multiple linearsystems of equations during each sweep, e.g. with a multigrid method. In thispaper, we present an inexact variant of SDC, where each solve of a linearsystem is replaced by a single multigrid V-cycle and thus significantly reducesthe cost for each sweep. For the investigated examples, this strategy resultsonly in a small increase of the number of required sweeps and we demonstratethat "inexact spectral deferred corrections" can provide a dramatic reductionof the overall number of multigrid V-cycles required to complete an SDC timestep.
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