新的四阶能量守恒积分器系列

IF 1.7 3区数学 Q2 MATHEMATICS, APPLIED

Numerical Algorithms Pub Date : 2024-04-23 DOI:10.1007/s11075-024-01824-w

Yuto Miyatake

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引用次数: 0

摘要

针对具有非对称结构矩阵的哈密顿系统，提出了一个新的四阶能量守恒积分器系列。这些积分器采用 Runge-Kutta 方法和连续级 Runge-Kutta 方法的组合形式，并具有一组自由参数，从而提供了更大的灵活性和更高的效率。具体来说，我们证明了通过仔细选择这些自由参数，应用于四阶积分器的简化牛顿迭代可以并行化。因此，与现有的四阶能量守恒积分器相比，积分器的速度更快、效率更高。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

A new family of fourth-order energy-preserving integrators

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A new family of fourth-order energy-preserving integrators

For Hamiltonian systems with non-canonical structure matrices, a new family of fourth-order energy-preserving integrators is presented. The integrators take a form of a combination of Runge–Kutta methods and continuous-stage Runge–Kutta methods and feature a set of free parameters that offer greater flexibility and efficiency. Specifically, we demonstrate that by carefully choosing these free parameters, a simplified Newton iteration applied to the integrators of order four can be parallelizable. This results in faster and more efficient integrators compared with existing fourth-order energy-preserving integrators.

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来源期刊

Numerical Algorithms 数学-应用数学

CiteScore

4.00

自引率

9.50%

发文量

201

审稿时长

9 months

期刊介绍： The journal Numerical Algorithms is devoted to numerical algorithms. It publishes original and review papers on all the aspects of numerical algorithms: new algorithms, theoretical results, implementation, numerical stability, complexity, parallel computing, subroutines, and applications. Papers on computer algebra related to obtaining numerical results will also be considered. It is intended to publish only high quality papers containing material not published elsewhere.