 Strang splitting

For finite matrices $A,B$, Strang splitting approximates the evolution $e^{h(A+B)}$ byIt advances the $A$ dynamics for a half step, the $B$ dynamics for a full step, and the $A$ dynamics for a half step. Expanding the three matrix exponentials givesso the one-step local truncation error is $O(h^3)$. Bounded propagation on a fixed time interval gives global error $O(h^2)$. The identity $S_{-h}=S_h^{-1}$ expresses time symmetry. Commuting matrices make the product exact.^[ref]

The finite-matrix assumptions are relevant when the method is applied after a spatial semidiscretization. Error constants can depend on the spatial mesh through commutators. A fixed-matrix second-order argument alone does not prove an error estimate uniform over increasingly fine spatial grids.