Improved error estimates of a new splitting scheme for charged-particle dynamics in strong magnetic field with maximal ordering

TL;DR

This paper presents a new explicit symmetric second-order splitting scheme for charged-particle dynamics in strong magnetic fields, offering improved error bounds and energy conservation.

Contribution

The paper introduces a novel splitting scheme with rigorous error analysis and demonstrated long-term energy conservation in strong magnetic field regimes.

Findings

Achieves uniform second-order error bounds in strong magnetic fields.

Numerical experiments confirm optimal convergence rates.

Method maintains near-conservation of energy over long simulations.

Abstract

This paper introduces a novel second-order splitting scheme for charged-particle dynamics in strong magnetic fields characterized by the maximal ordering. The proposed scheme is explicit and symmetric, which respectively ensure the efficiency of the algorithm and its long-term near-conservation of energy. We rigorously prove that the scheme achieves improved error bounds for both the position and the velocity component parallel to the magnetic field, yielding a uniform second-order error bound under specific strong-field regimes. Numerical experiments confirm the optimal convergence rates and the long-term energy near conservation of the method.