Explicit Symmetric Exponential Integrators for Charged-Particle Dynamics in a Strong and Constant Magnetic Field

In this paper, we derive and analyze symmetric exponential integrators for charged-particle dynamics in a strong and constant magnetic field. We first present the scheme of exponential integrators and then establish the symmetry conditions for the methods. Explicit symmetric exponential integrators up to order four are constructed on the basis of the symmetry conditions. In order to show the remarkable performances of new symmetric methods in comparison with symmetric Runge–Kutta methods including the 2-stage Gauss method, two numerical experiments are carried out and the numerical results demonstrate the super numerical behavior.