English

An Explicit Symmetric Exponential Integrator and Its Error Estimate for the Relativistic Charged-Particle Dynamics

Numerical Analysis 2026-03-24 v1 Numerical Analysis

Abstract

This paper investigates the equations of motion for a relativistic charged particle in a general magnetic field. By reformulating the dynamics in four-dimensional spacetime and separating the linear and nonlinear parts, we construct an explicit symmetric exponential integrator based on Lie splitting. Rigorous analysis establishes its unconditional stability and second-order convergence. Numerical experiments confirm its superior performance, including accuracy, effciency and long-time Hamiltonian conservation.

Keywords

Cite

@article{arxiv.2603.21137,
  title  = {An Explicit Symmetric Exponential Integrator and Its Error Estimate for the Relativistic Charged-Particle Dynamics},
  author = {Zhirui Shen and Bin Wang},
  journal= {arXiv preprint arXiv:2603.21137},
  year   = {2026}
}