Discrete line integral method for the Lorentz force system

TL;DR

This paper introduces a discrete line integral method for solving the Lorentz force system, which conserves energy exactly for certain polynomial Hamiltonians and approximately otherwise, showing advantages over traditional methods.

Contribution

The paper presents a novel energy-preserving numerical method based on Boole's discrete line integral for the Lorentz force system, especially effective for polynomial Hamiltonians of degree up to four.

Findings

Exact energy conservation for polynomial Hamiltonians of degree ≤ 4

Approximate energy conservation in other cases

Numerical experiments demonstrate the method's effectiveness

Abstract

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 $\nu \leq 4$. 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.