Efficient symplectic integrators for cubic and quartic potentials
This work provides more efficient numerical integration for Hamiltonian systems with polynomial potentials, which is relevant for computational physics and dynamical systems.
The authors develop new high-order symplectic integrators for Hamiltonian systems with cubic or quartic potentials, achieving improved efficiency over existing methods by exploiting the reduced number of order conditions for polynomial potentials.
We present a set of new, efficient high-order symplectic methods designed for Hamiltonian systems with cubic or quartic potentials. By demonstrating that polynomial potentials require fewer order conditions, we develop schemes that outperform both standard symmetric compositions of second-order methods and existing RKN splitting methods. Numerical results confirm their improved efficiency over state-of-the-art alternatives found in the literature.