On Symmetrical Methods for Charged Particle Dynamics

Renxuan Tang,Dongfang Li

doi:10.3390/sym13091626

Abstract

In this paper, we use the scalar auxiliary variable (SAV) approach to rewrite the charged particle dynamics as a new family of ODE systems. The systems own a conserved energy. It is shown that a family of symmetrical methods is energy-conserving for a new ODE system but may not be for the original systems. Moreover, the methods have high-order accuracy. Numerical results are given to confirm the theoretical findings.

Highlights

IntroductionWe are interested in investigating high-order numerical methods for solving the following charged particle dynamics [1,2,3,4]:
We are interested in investigating high-order numerical methods for solving the following charged particle dynamics [1,2,3,4]: q = p, p = p × L(q) − ∇U(q), q(0) = q0, p(0) = p0, (q0, p0) ∈ Ω ⊆ R3 × R3, (1)
We propose a novel approach to developing some energy-conserving numerical methods for the charged particle dynamics

Summary

Introduction

We are interested in investigating high-order numerical methods for solving the following charged particle dynamics [1,2,3,4]:. The main results indicate that the method preserves polynomial Hamiltonians. The numerical methods may not exactly be energy-conserving. In this short paper, we propose a novel approach to developing some energy-conserving numerical methods for the charged particle dynamics. It can be seen that certain Runge–Kutta methods are energy-conserving for the ODE system, while the same Runge–Kutta methods cannot generally preserve the energy of the original system (1).

Energy-Conserving Methods

Summary