Long term analysis of splitting methods for charged-particle dynamics

TL;DR

This paper provides a rigorous long-term analysis of splitting methods for charged-particle dynamics, focusing on their energy, momentum, and magnetic moment conservation properties under specific conditions.

Contribution

It introduces a backward error analysis approach to derive modified equations and invariants, proving near-conservation over long times for these numerical methods.

Findings

Splitting methods nearly conserve invariants over long times under constant magnetic fields.

Modified equations and invariants are derived using backward error analysis.

Numerical experiments confirm theoretical long-term conservation properties.

Abstract

In this paper, we rigorously analyze the energy, momentum and magnetic moment behaviours of two splitting methods for solving charged-particle dynamics. The near-conservations of these invariants are given for the system under constant magnetic field or quadratic electric potential. By the approach named as backward error analysis, we derive the modified equations and modified invariants of the splitting methods and based on which, the near-conservations over long times are proved. Some numerical experiments are presented to demonstrate these long time behaviours.