Improved error estimates of a new splitting scheme for charged-particle dynamics in strong magnetic field with maximal ordering
For computational plasma physics, this provides a more efficient and accurate numerical method for simulating charged particles in strong magnetic fields.
This paper proposes a new explicit, symmetric second-order splitting scheme for charged-particle dynamics in strong magnetic fields with maximal ordering, achieving uniform second-order error bounds for position and parallel velocity. Numerical experiments confirm optimal convergence and long-term energy near-conservation.
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.