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

2015/01/18 by Kristian Mads Egeris Nielsen, Nielsen, Kristian Mads Egeris
Computer Science · Mathematics · #Computational Physics (physics.comp-ph) #FOS: Physical sciences #Modeling and Simulation Systems #Numerical methods for differential equations #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.1501.04345

openalex publication_date 2015/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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