Discrete line integral method for the Lorentz force system

In this paper, we apply the Boole discrete line integral to solve the Lorentz force system which is written as a non-canonical Hamiltonian system. The method is exactly energy-conserving for polynomial Hamiltonians of degree $ν\leq 4$. In any other case, the energy can also be conserved approximatively. With comparison to well-used Boris method, numerical experiments are presented to demonstrate the energy-preserving property of the method.

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