Relationship between vanishing splitting errors and pairwise commutativity Original Research Article

It has been shown that the commutativity of the two sub-operators in different operator splitting discretizations implies zero splitting error. This work investigates whether this commutativity condition is necessary for zero splitting error for some given operator splittings. The case of more than two sub-operators is also discussed, but there are still some open problems (see the end of this work).