Trigonometrically fitted two-derivative Runge-Kutta-Nystroem methods for second-order oscillatory differential equations

Chen Zhaoxia; Shi Lei; Liu Siyao; You Xiong

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Trigonometrically fitted two-derivative Runge-Kutta-Nystroem methods for second-order oscillatory differential equations

机译：二阶振荡微分方程的三角拟合二阶Runge-Kutta-Nystroem方法

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摘要

A new family of modified two-derivative Runge-Kutta-Nystrom (TDRKN) methods are proposed for solving initial value problems of second-order oscillatory ordinary differential equations. Order conditions are obtained via the Nystrom tree theory and the B-series theory. Trigonometric fitting conditions are derived. Two practical explicit trigonometrically fitted TDRKN (TFTDRKN) methods are constructed. The phase properties of the new integrators are examined and their periodicity regions are obtained. The results of numerical experiments show the efficiency and competence of the new methods compared with some highly efficient codes in the literature. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.

机译：提出了一种新的改进的二阶导数Runge-Kutta-Nystrom（TDRKN）方法来解决二阶振荡常微分方程的初值问题。通过Nystrom树理论和B系列理论获得有序条件。得出三角拟合条件。构造了两种实用的显式三角拟合TDRKN（TFTDRKN）方法。检查了新积分器的相位特性，并获得了它们的周期性区域。数值实验结果表明，与文献中一些高效代码相比，新方法的有效性和竞争力。（C）2019年IMACS。由Elsevier B.V.发布。保留所有权利。

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来源
《Applied numerical mathematics》 |2019年第8期|171-189|共19页
作者
Chen Zhaoxia; Shi Lei; Liu Siyao; You Xiong;
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作者单位

Nanjing Agr Univ, Coll Sci, Nanjing 210095, Jiangsu, Peoples R China;

Nanjing Agr Univ, Coll Sci, Nanjing 210095, Jiangsu, Peoples R China;

Nanjing Agr Univ, Coll Sci, Nanjing 210095, Jiangsu, Peoples R China;

Nanjing Agr Univ, Coll Sci, Nanjing 210095, Jiangsu, Peoples R China;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Two-derivative Runge-Kutta-Nystrom method; Nystrom tree; B-series; Order condition; Trigonometrical fitting; Periodicity region;

机译：二阶导数Runge-Kutta-Nystrom方法;Nystrom树;B系列;有序条件;三角拟合;周期区域;

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专利

1. Trigonometrically fitted two-derivative Runge-Kutta methods for solving oscillatory differential equations [J] . Yonglei Fang, Xiong You, Qinghe Ming Numerical algorithms . 2014,第3期

机译：三角拟合二阶Runge-Kutta方法求解振动微分方程
2. New optimized symmetric and symplectic trigonometrically fitted RKN methods for second-order oscillatory differential equations [J] . Chen Zhaoxia, Zhang Ruqiang, Shi Wei, International journal of computer mathematics . 2017,第5a8期

机译：二阶振荡微分方程的新优化对称对称辛三角拟合RKN方法
3. A Four-Stage Fifth-Order Trigonometrically Fitted Semi-Implicit Hybrid Method for Solving Second-Order Delay Differential Equations [J] . Ahmad Sufia Zulfa, Ismail Fudziah, Senu Norazak Mathematical Problems in Engineering . 2016,第pta6期

机译：二阶时滞微分方程的四阶五阶三角拟合半隐式混合方法
4. A Trigonometrically Fitted Optimized Two-step Hybrid Block Method for Solving Initial-value Problems of the Form y" = f(x,y,y') with Oscillatory Solutions [C] . Higinio Ramos, Z. Kalogiratou, Th. Monovasilis, International Conference on Numerical Analysis and Applied Mathematics . 2015

机译：具有振荡溶液的求解y“= f（x，y，y'）的初始值问题的三角拟合的两步混合块方法
5. DYNAMICALLY FILTERED LINEAR MULTI-STEP METHODS AND THE COMPUTATION OF SMOOTH SOLUTIONS OF OSCILLATORY STIFF ORDINARY DIFFERENTIAL EQUATIONS. [D] . MAJDA, GEORGE JOSEPH. 1980

机译：动态滤波线性多步法和振动刚度常微分方程的光滑解的计算。
6. Exponentially Fitted Two-Derivative Runge-Kutta Methods for Simulation of Oscillatory Genetic Regulatory Systems [O] . Zhaoxia Chen, Juan Li, Ruqiang Zhang, 2015

机译：振荡遗传调控系统的指数拟合二阶Runge-Kutta方法
7. Trigonometric collocation methods based on Lagrange basis polynomials for multi-frequency oscillatory second-order differential equations [O] . Wang, Bin, Wu, Xinyuan, Meng, Fanwei 2016

机译：基于拉格朗日基多项式的三角配置方法用于多频振荡二阶微分方程
8. Classical Eighth- and Lower-Order Runge-Kutta-Nystroem Formulas with a New Stepsize Control Procedure for Special Second-Order Differential Equations [R] . Fehlberg, E. 1973

机译：具有特殊二阶微分方程新步长控制过程的经典八阶和低阶Runge-Kutta-Nystroem公式

Trigonometrically fitted two-derivative Runge-Kutta-Nystroem methods for second-order oscillatory differential equations

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