= Strang splitting
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For finite <matrices> $A,B$, Strang splitting approximates the evolution $e^{h(A+B)}$ by
$$
S_h=e^{hA/2}e^{hB}e^{hA/2}.
$$
It 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> gives
$$
S_h=I+h(A+B)+\tfrac12h^2(A+B)^2+O(h^3),
$$
so 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.<Splitting methods with complex coefficients by Sergio Blanes and others>[§1, equation(5), printed p2]{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.
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