Efficient symplectic integrators for cubic and quartic potentials

TL;DR

The paper introduces new high-order symplectic integrators optimized for Hamiltonian systems with cubic or quartic potentials, outperforming existing methods in efficiency.

Contribution

Development of novel high-order symplectic methods tailored for polynomial potentials, reducing order conditions and enhancing computational efficiency.

Findings

New integrators outperform standard symmetric composition methods.

Numerical tests confirm improved efficiency over existing algorithms.

Polynomial potentials require fewer order conditions, simplifying scheme design.

Abstract

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.