The Construction and Optimal Error Analysis of Explicit Energy-Preserving Methods for Charged Particle Dynamics Under Strong Magnetic Field

In this study, combining the idea of splitting and relaxation, a first-order Lie-Trotter splitting scheme and a second-order Strang splitting scheme are constructed for the charged-particle dynamics in the presence of a strong magnetic field. Both the schemes are explicit and energy-preserving. For the maximal ordering scaling regime, a uniform (with respect to the magnetic field strength) and optimal error bound for both the position and the velocity component parallel to the magnetic field are established for the proposed first-order Lie-Trotter splitting scheme. Numerical experiments are carried out to demonstrate the optimal error and energy conservation properties of the proposed splitting schemes.