Poisson Integrators based on splitting method for Poisson systems

TL;DR

This paper introduces Poisson integrators based on splitting methods for separable Poisson systems, demonstrating their superior performance over non-Poisson integrators in phase orbit tracking and energy conservation.

Contribution

It develops new Poisson integrators tailored for separable systems using splitting methods, enhancing numerical accuracy and efficiency.

Findings

Outperforms higher order non-Poisson integrators in phase orbit tracking

Provides better long-term energy conservation

Achieves higher efficiency in numerical simulations

Abstract

We propose Poisson integrators for the numerical integration of separable Poisson systems. We analyze three situations in which the Poisson systems are separated in three ways and the Poisson integrators can be constructed by using the splitting method. Numerical results show that the Poisson integrators outperform the higher order non-Poisson integrators in phase orbit tracking, long-term energy conservation and efficiency.