On the necessity of negative coefficients for operator splitting schemes of order higher than two
For an autonomous ordinary differential equation that is separable in solvable parts, operator splitting methods are known to be useful numerical tools. It is known that such methods must have negative coefficients if their order is \(\geq 3\). The authors give an instructive and elementary proof of this fact. The technique of the proof allows to draw useful additional conclusions about, e.g., the distribution of the negative coefficients. Moreover, examples are given showing that higher order schemes without negative coefficients exist for a slightly different class of differential equations.
scientific article; zbMATH DE number 2173598