SIAM Journal on Numerical Analysis, Volume 59, Issue 4, Page 2075-2105, January 2021.
In this work, we consider the error estimates of some splitting schemes for the charged-particle dynamics under a strong magnetic field. We first propose a novel energy-preserving splitting scheme with computational cost per step independent of the strength of the magnetic field. Then under the maximal ordering scaling case, we establish for the scheme and in fact for a class of Lie--Trotter-type splitting schemes a uniform (in the strength of the magnetic field) and optimal error bound in the position and in the velocity parallel to the magnetic field. For the general strong magnetic field case, the modulated Fourier expansions of the exact and the numerical solutions are constructed to obtain a favorable dependence of the error on the strength of the magnetic field. Numerical experiments are presented to illustrate the error and energy behavior of the splitting schemes.

中文翻译：

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强磁场下带电粒子动力学的一些分裂方案的误差估计

SIAM 数值分析杂志，第 59 卷，第 4 期，第 2075-2105 页，2021 年 1 月。
在这项工作中，我们考虑了强磁场下带电粒子动力学的一些分裂方案的误差估计。我们首先提出了一种新的节能分裂方案，其每步的计算成本与磁场强度无关。然后在最大排序标度的情况下，我们为该方案和实际上为一类 Lie--Trotter 型分裂方案建立了一个均匀的（在磁场强度上）和最佳的位置和速度误差界平行于磁场。对于一般强磁场情况，构建精确解和数值解的调制傅立叶展开以获得误差对磁场强度的有利依赖性。