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arXiv · 2603.21137

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

Zhirui Shen·Bin Wang
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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.

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Zhirui Shen, Bin Wang. 2026-03-22. An Explicit Symmetric Exponential Integrator and Its Error Estimate for the Relativistic Charged-Particle Dynamics. https://arxiv.org/abs/2603.21137

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