The combined spatiotemporal iterative operator-splitting method combines the Schwarz waveform-relaxation and the iterative operator-splitting method.
The following algorithm iterates with a ﬁxed splitting discretization step size τ . On the time interval [tn, tn+1], we solve the following subproblems consecutively for i = 1, 3, . . .2m+1 and j = 1, 3, . . . 2m+1. In this notation, i represents the iteration index for the temporal splitting and j represents the iteration index for the spatial splitting.