Efficient fourth order symplectic integrators for near-harmonic separable Hamiltonian systems

TL;DR

This paper introduces new efficient fourth order symplectic integrators specifically designed for near-harmonic separable Hamiltonian systems, demonstrating superior performance over existing methods through numerical tests.

Contribution

The paper develops novel symmetric splitting coefficients for fourth order integrators tailored to near-harmonic systems, improving accuracy and efficiency.

Findings

Integrators outperform previous methods in accuracy.

Numerical tests confirm improved performance.

Methods are efficient for common Hamiltonian systems.

Abstract

Efficient fourth order symplectic integrators are proposed for numerical integration of separable Hamiltonian systems H(p,q)=T(p)+V(q). Symmetric splitting coefficients with five to nine stages are obtained by higher order decomposition of the simple harmonic oscillator. The performance of the methods is evaluated for various Hamiltonian systems: Integration errors are compared to those of acclaimed integrators composed by S. Blanes et al. (2013), W. Kahan et al. (1999) and H. Yoshida (1990). Numerical tests indicate that the integrators obtained in this paper perform significantly better than previous integrators for common Hamiltonian systems.