Tests of the approximations made in sCOLA for the density field and the gravitational potential. As in Fig. 5, the diagnostic tools are the power spectrum relative to tCOLA (top panel) and the cross-correlation with tCOLA (bottom panel). Our sCOLA algorithm uses the approximate interior density field δ^sCOLA and the LEP approximation for the boundary gravitational potential (dash-dotted blue line). In other simulations, as indicated in the legend, we use the true density field δ and/or the true gravitational potential Φ at the boundaries. The approximation made for the density field dominates, especially at large scales.