Explicit symplectic algorithms based on generating functions for charged   particle dynamics
  Dynamics of a charged particle in the canonical coordinates is a Hamiltonian system, and the well-known symplectic algorithm has been regarded as the de facto method for numerical integration of Hamiltonian systems due to its long-term accuracy and fidelity. For long-term simulations with high efficiency, explicit symplectic algorithms are desirable. However, it is widely accepted that explicit symplectic algorithms are only available for sum-separable Hamiltonians, and that this restriction severely limits the application of explicit symplectic algorithms to charged particle dynamics. To overcome this difficulty, we combine the familiar sum-split method and a generating function method to construct second and third order explicit symplectic algorithms for dynamics of charged particle. The generating function method is designed to generate explicit symplectic algorithms for product-separable Hamiltonian with form of $H(\mathbf{p},\mathbf{q})=\mathbf{p}_{i}f(\mathbf{q})$ or $H(\mathbf{p},\mathbf{q})=\mathbf{q}_{i}f(\mathbf{p})$. Applied to the simulations of charged particle dynamics, the explicit symplectic algorithms based on generating functions demonstrate superiorities in conservation and efficiency. 
Ruili Zhang, Hong Qin, Yifa Tang, Jian Liu, Yang He, Jianyuan Xiao
physics.plasm-ph