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In this paper, we offer a comparison in terms of computational efficiencybetween two techniques to avoid order reduction when using Strang method tointegrate nonlinear initial boundary value problems with time-dependentboundary conditions. Considering different implementations for each of thetechniques, we show that the technique suggested by Alonso et al. is moreefficient than the one suggested by Einkemmer et al. Moreover, for one of theimplementations of the technique by Alonso et al. we justify its order throughthe proof of some new theorems.

Looking for efficiency when avoiding order reduction in nonlinear problems with Strang splitting