The aim of this paper is to formulate and analyze numerical discretizations of charged-particle dynamics (CPD) in a strong nonuniform magnetic field. A strategy is firstly performed for the two dimensional CPD to construct the semi-discretization and full-discretization which have optimal accuracy. This accuracy is improved in the position and in the velocity when the strength of the magnetic field becomes stronger. This is a better feature than the usual so called "uniformly accurate methods". To obtain this refined accuracy, some reformulations of the problem and two-scale exponential integrators are incorporated, and the optimal accuracy is derived from this new procedure. Then based on the strategy given for the two dimensional case, a new class of uniformly accurate methods with simple scheme is formulated for the three dimensional CPD in maximal ordering case. All the theoretical results of the accuracy are numerically illustrated by some numerical tests.

翻译：本文的目的是在强大的非统一磁场中制定和分析充电粒子动态(CPD)的数字分解。 首先,为两维的CPD执行了一项战略,以构建半分解和完全分解,且具有最佳准确性。当磁场强度变强时,这种精确度在位置和速度上都有提高。这比通常所谓的“统一准确方法”要好。为了获得这种精细的准确性,对问题和两个尺度的指数集成器进行了一些重新配方,并从这一新程序得出了最佳的准确性。然后,根据对两维的CPD给出的战略,在最大定购案的情况下,为三维的CPD制定了一种新的统一准确方法,在最大定购案中,为三维的CPD制定了新的统一精确方法。准确性的所有理论结果都是用数字测试来说明的。