Explicit, time-reversible and symplectic integrator for Hamiltonians in isotropic uniformly curved geometries

2021/04/22 by Ana Cannas da Silva, Silva, Ana, Eitan Ben Av +3
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Chaotic Dynamics (nlin.CD) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2104.10908

openalex publication_date 2021/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The kinetic term of the N-body Hamiltonian system defined on the surface of the sphere is non-separable. As a result, standard explicit symplectic integrators are inapplicable. We exploit an underlying hierarchy in the structure of the kinetic term to construct an explicit time-reversible symplectic scheme of second order. We use iterative applications of the method to construct a fourth order scheme and demonstrate its efficiency.

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