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The aim of this paper is to formulate and analyze numerical discretizationsof charged-particle dynamics (CPD) in a strong nonuniform magnetic field. Astrategy is firstly performed for the two dimensional CPD to construct thesemi-discretization and full-discretization which have optimal accuracy. Thisaccuracy is improved in the position and in the velocity when the strength ofthe magnetic field becomes stronger. This is a better feature than the usual socalled "uniformly accurate methods". To obtain this refined accuracy, somereformulations of the problem and two-scale exponential integrators areincorporated, and the optimal accuracy is derived from this new procedure. Thenbased on the strategy given for the two dimensional case, a new class ofuniformly accurate methods with simple scheme is formulated for the threedimensional CPD in maximal ordering case. All the theoretical results of theaccuracy are numerically illustrated by some numerical tests.

Semi-discretization and full-discretization with optimal accuracy for charged-particle dynamics in a strong nonuniform magnetic field