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

TL;DR

This paper introduces an explicit symmetric exponential integrator for relativistic charged-particle dynamics, demonstrating its stability, accuracy, and efficiency through theoretical analysis and numerical experiments.

Contribution

It presents a novel explicit symmetric exponential integrator based on Lie splitting for relativistic particle equations, with proven stability and second-order convergence.

Findings

Unconditional stability of the integrator

Second-order convergence established

Superior performance in accuracy and long-term energy conservation

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.