Strang splitting

Strang splitting approximates $e^{h(A+B)}$ by $e^{hA/2}{e}^{hB}{e}^{hA/2}$. Its time symmetry cancels the quadratic local commutator defect, giving local error $O(h^3)$ and global order two.

If $S_h$ is a symmetric second-order splitting, then $S_{\gamma h}{S}_{\delta h}{S}_{\gamma h}$ is fourth order for $\gamma =(2-2^{1/3}{)}^{-1}$ and $\delta =-2^{1/3}(2-2^{1/3}{)}^{-1}$. The identities $2\gamma +\delta =1$ and $2{\gamma }^3+{\delta }^3=0$ preserve the total step and cancel the leading odd defect.