Symmetric Adaptive Higher-Order Energy-Preserving Methods for a Charged Particle System and Guiding Center System

IF 2.2 3区 综合性期刊 Q2 MULTIDISCIPLINARY SCIENCES
Symmetry-Basel Pub Date : 2023-10-24 DOI:10.3390/sym15111969
Beibei Zhu, Hongji Zhou
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引用次数: 0

Abstract

We propose higher-order adaptive energy-preserving methods for a charged particle system and a guiding center system. The higher-order energy-preserving methods are symmetric and are constructed by composing the second-order energy-preserving methods based on the averaged vector field. In order to overcome the energy drift problem that occurs in the energy-preserving methods based on the average vector field, we develop two adaptive algorithms for the higher-order energy-preserving methods. The two adaptive algorithms are developed based on using variable points of Gauss–Legendre’s quadrature rule and using two different stepsizes. The numerical results show that the two adaptive algorithms behave better in phase portrait and energy conservation than the Runge–Kutta methods. Moreover, it is shown that the energy errors obtained by the two adaptive algorithms can be bounded by the machine precision over long time and do not show energy drift.
带电粒子系统和导向中心系统的对称自适应高阶能量守恒方法
我们提出了带电粒子系统和导向中心系统的高阶自适应能量守恒方法。高阶保能方法是对称的,由基于平均向量场的二阶保能方法组合而成。为了克服基于平均向量场的能量守恒方法中存在的能量漂移问题,我们开发了两种高阶能量守恒方法的自适应算法。基于高斯-勒让德正交规则的可变点,采用两种不同的步长,提出了两种自适应算法。数值结果表明,两种自适应算法在相位刻画和能量节约方面都优于龙格-库塔方法。结果表明,两种自适应算法得到的能量误差在较长时间内都能以机器精度为界,且不存在能量漂移。
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来源期刊
Symmetry-Basel
Symmetry-Basel MULTIDISCIPLINARY SCIENCES-
CiteScore
5.40
自引率
11.10%
发文量
2276
审稿时长
14.88 days
期刊介绍: Symmetry (ISSN 2073-8994), an international and interdisciplinary scientific journal, publishes reviews, regular research papers and short notes. Our aim is to encourage scientists to publish their experimental and theoretical research in as much detail as possible. There is no restriction on the length of the papers. Full experimental and/or methodical details must be provided, so that results can be reproduced.
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