Abstract
With the natural splitting of a Hamiltonian system into kinetic energy and potential energy, we construct two new optimal thirdorder force-gradient symplectic algorithms in each of which the norm of fourth-order truncation errors is minimized. They are both not explicitly superior to their no-optimal counterparts in the numerical stability and the topology structure-preserving, but they are in the accuracy of energy on classical problems and in one of the energy eigenvalues for one-dimensional time-independent Schrödinger equations. In particular, they are much better than the optimal third-order non-gradient symplectic method. They also have an advantage over the fourth-order non-gradient symplectic integrator.
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Li, R., Wu, X. Optimized third-order force-gradient symplectic algorithms. Sci. China Phys. Mech. Astron. 53, 1600–1609 (2010). https://doi.org/10.1007/s11433-010-4074-2
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DOI: https://doi.org/10.1007/s11433-010-4074-2