1.75D ambipolar MHD wave test, where fast waves move upward against gravity. Left: vertical velocity profile for the two STS and three different splitting approaches and for an explicit reference run. Right: normalized error, 6, from Eq. (14) as a function of the cell size, comparing the numerical solution obtained using STS with a reference numerical solution obtained in an explicit implementation. All variants produce nearly identical results, such that all curves seem to be overlapping.