# High-order energy-conserving Line Integral Methods for charged particle dynamics

## TL;DR

This paper develops high-order energy-conserving numerical methods based on Line Integral Methods for accurately simulating charged particle dynamics while preserving energy, extending the framework of Hamiltonian Boundary Value Methods.

## Contribution

It introduces a new class of high-order energy-conserving methods for charged particles within the LIM framework, expanding the applicability of HBVMs.

## Key findings

- Methods preserve energy accurately over long simulations
- Numerical tests confirm theoretical properties
- High-order methods outperform lower-order counterparts

## Abstract

In this paper we study arbitrarily high-order energy-conserving methods for simulating the dynamics of a charged particle. They are derived and studied within the framework of Line Integral Methods (LIMs), previously used for defining Hamiltonian Boundary Value Methods (HBVMs), a class of energy-conserving Runge-Kutta methods for Hamiltonian problems. A complete analysis of the new methods is provided, which is confirmed by a few numerical tests.