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math.NA2026
High-order uniformly accurate fully discrete schemes with long time near-conservations for two nonlinear coupled dispersive models in the nonrelativistic regime
Lina Wang, Jiyong Li, Bin Wang
Nonlinear coupled dispersive models arise in numerous physical settings, including quantum electrodynamics, nonlinear optics, and plasma dynamics. In the nonrelativistic limit, suc…
math.NA2026
Improved error estimates of a new splitting scheme for charged-particle dynamics in strong magnetic field with maximal ordering
Mengting Hu, Jiyong Li, Bin Wang
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 ex…
math.NA2025
Fourth-order uniformly accurate integrators with long time near conservations for the nonlinear Dirac equation in the nonrelativistic regime
Lina Wang, Bin Wang, Jiyong Li
In this paper, we propose two novel fourth-order integrators that exhibit uniformly high accuracy and long-term near conservations for solving the nonlinear Dirac equation (NLDE) i…