Convergence of some conservative Strang splitting methods for Charged-Particle Dynamics under a strong magnetic field

Abstract

In this study, we analyze the error estimates for different splitting schemes used in modeling Charged-Particle Dynamics within a strong magnetic field. We introduce an energy-preserving splitting scheme whose per-step computational cost remains unaffected by the magnetic field’s strength. For the maximal ordering scaling case, we establish an error bound for this scheme, and more broadly for a range of Strang splitting schemes, in terms of both position and velocity, which is proportional to the step size $h$. Additionally, we provide an error bound for position and velocity related to the parameter $\varepsilon$, although this bound is not the most optimal. Numerical experiments are conducted to demonstrate the error characteristics of these splitting schemes, revealing that the error bound exhibits a negative half-order dependence on $\varepsilon$.