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Prior to the recent development of symplectic integrators, the time-stepping operator $\text{e}^{h(A+B)}$ was routinely decomposed into a sum of products of $\text{e}^{\text hA}$ and $\text{e}^{\text hB}$ in the study of hyperbolic partial differential equations. In the context of solving Hamiltonian dynamics, we show that such a decomposition gives rise to both even- and odd-order Runge–Kutta and...

Multi-product operator splitting as a general method of solving autonomous and nonautonomous equations