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

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.