A novel class of high-order uniformly accurate exponential integrators with local linear extension for the charged-particle dynamics under strong magnetic field

@misc{wang2026novel,
  title = {{A novel class of high-order uniformly accurate exponential integrators with local linear extension for the charged-particle dynamics under strong magnetic field}},
  author = {Lina Wang and Bin Wang and Beibei Zhu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.04478},
  eprint = {2606.04478},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.04478},
}

TY  - UNPB
TI  - A novel class of high-order uniformly accurate exponential integrators with local linear extension for the charged-particle dynamics under strong magnetic field
AU  - Lina Wang
AU  - Bin Wang
AU  - Beibei Zhu
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2606.04478
UR  - https://arxiv.org/abs/2606.04478
AB  - In this paper, we develop a novel class of high-order uniformly accurate exponential integrators for charged-particle dynamics under strong magnetic field. The small parameter 0<ε≪ 1 induces rapid temporal oscillations, rendering traditional numerical methods prohibitively expensive due to severe step-size restrictions. To address this issue, a linearization technology that introduces auxiliary polynomial variables is employed to recast the original charged-particle dynamics as a higher-dimensional system. Classical exponential integrators are subsequently applied to this augmented formulation, which inherently carries richer structural information, thereby yielding a family of uniformly accurate exponential integrators that can reach arbitrarily high order without requiring any order conditions. For strong magnetic fields under the maximal-ordering scaling, we rigorously establish through algebraic techniques that the schemes with auxiliary polynomial variables of degree k≥2 achieve an improved position error bound of 𝒪(min{ε^k+1h,ε h^k+1}) and a uniform velocity error bound of 𝒪(min{ε^kh,h^k+1}), where h denotes the time-step size. Under the additional condition that the magnetic field gradient vanishes at the origin, these bounds sharpen to 𝒪(min{ε^k+2,ε h^k+1}) and 𝒪(min{ε^k+1,h^k+1}) for the position and velocity, respectively, for k≥1. The same sharper bounds hold for constant strong magnetic fields. Numerical experiments confirm the advantages of the proposed methods.
ER  -