A novel directly energy-preserving method for charged particle dynamics

In this paper, we apply the coordinate increment discrete gradient (CIDG) method to solve the Lorentz force system which can be written as a non-canonical Hamiltonian system. Then we can obtain a new energy-preserving CIDG-I method for the system. The CIDG-I method can combine with its adjoint method CIDG-II which is also a energy-preserving method to form a new method, namely CIDG-C method. The CIDG-C method is symmetrical and can conserve the Hamiltonian energy directly and exactly. With comparison to the well-used Boris method, numerical experiments indicate that the CIDG-C method holds advantage over the Boris method in terms of energy-conserving. The Fig. 5(b) in the original paper contains an error. We submit the correct Fig. 5(b) and an errata in this paper, which is described in remark4.1.