Two-step extended RKN methods for oscillatory systems

Jiyong Li; Bin Wang; Xiong You; Xinyuan Wu

doi:10.1016/j.cpc.2011.07.007

Two-step extended RKN methods for oscillatory systems

Jiyong Li
, Bin Wang
, Xiong You
, Xinyuan Wu

Research output: Contribution to journal › Article › peer-review

37 Scopus citations

Abstract

In this paper, two-step extended Runge-Kutta-Nyström-type methods for the numerical integration of perturbed oscillators are presented and studied. The new methods inherit the framework of two-step hybrid methods and are adapted to the special feature of the true flows in both the internal stages and the updates. Based on the EN-trees theory [H.L. Yang, X.Y. Wu, X. You, Y.L. Fang, Extended RKN-type methods for numerical integration of perturbed oscillators, Comput. Phys. Comm. 180 (2009) 1777-1794], order conditions for the new methods are derived via the ^BBT-series defined on the set BT of branches and the ^BBWT-series defined on the subset BWT of BT. The stability and phase properties are analyzed. Numerical experiments show the applicability and efficiency of our new methods in comparison with the well-known high quality methods proposed in the scientific literature.

Original language	English
Pages (from-to)	2486-2507
Number of pages	22
Journal	Computer Physics Communications
Volume	182
Issue number	12
DOIs	https://doi.org/10.1016/j.cpc.2011.07.007
State	Published - Dec 2011
Externally published	Yes

Keywords

-series
-series
Order conditions
Oscillatory systems
Two-step extended Runge-Kutta-Nyström-type methods

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10.1016/j.cpc.2011.07.007

Cite this

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title = "Two-step extended RKN methods for oscillatory systems",

abstract = "In this paper, two-step extended Runge-Kutta-Nystr{\"o}m-type methods for the numerical integration of perturbed oscillators are presented and studied. The new methods inherit the framework of two-step hybrid methods and are adapted to the special feature of the true flows in both the internal stages and the updates. Based on the EN-trees theory [H.L. Yang, X.Y. Wu, X. You, Y.L. Fang, Extended RKN-type methods for numerical integration of perturbed oscillators, Comput. Phys. Comm. 180 (2009) 1777-1794], order conditions for the new methods are derived via the BBT-series defined on the set BT of branches and the BBWT-series defined on the subset BWT of BT. The stability and phase properties are analyzed. Numerical experiments show the applicability and efficiency of our new methods in comparison with the well-known high quality methods proposed in the scientific literature.",

keywords = "-series, -series, Order conditions, Oscillatory systems, Two-step extended Runge-Kutta-Nystr{\"o}m-type methods",

author = "Jiyong Li and Bin Wang and Xiong You and Xinyuan Wu",

year = "2011",

month = dec,

doi = "10.1016/j.cpc.2011.07.007",

language = "英语",

volume = "182",

pages = "2486--2507",

journal = "Computer Physics Communications",

issn = "0010-4655",

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}

TY - JOUR

T1 - Two-step extended RKN methods for oscillatory systems

AU - Li, Jiyong

AU - Wang, Bin

AU - You, Xiong

AU - Wu, Xinyuan

PY - 2011/12

Y1 - 2011/12

N2 - In this paper, two-step extended Runge-Kutta-Nyström-type methods for the numerical integration of perturbed oscillators are presented and studied. The new methods inherit the framework of two-step hybrid methods and are adapted to the special feature of the true flows in both the internal stages and the updates. Based on the EN-trees theory [H.L. Yang, X.Y. Wu, X. You, Y.L. Fang, Extended RKN-type methods for numerical integration of perturbed oscillators, Comput. Phys. Comm. 180 (2009) 1777-1794], order conditions for the new methods are derived via the BBT-series defined on the set BT of branches and the BBWT-series defined on the subset BWT of BT. The stability and phase properties are analyzed. Numerical experiments show the applicability and efficiency of our new methods in comparison with the well-known high quality methods proposed in the scientific literature.

AB - In this paper, two-step extended Runge-Kutta-Nyström-type methods for the numerical integration of perturbed oscillators are presented and studied. The new methods inherit the framework of two-step hybrid methods and are adapted to the special feature of the true flows in both the internal stages and the updates. Based on the EN-trees theory [H.L. Yang, X.Y. Wu, X. You, Y.L. Fang, Extended RKN-type methods for numerical integration of perturbed oscillators, Comput. Phys. Comm. 180 (2009) 1777-1794], order conditions for the new methods are derived via the BBT-series defined on the set BT of branches and the BBWT-series defined on the subset BWT of BT. The stability and phase properties are analyzed. Numerical experiments show the applicability and efficiency of our new methods in comparison with the well-known high quality methods proposed in the scientific literature.

KW - -series

KW - Order conditions

KW - Oscillatory systems

KW - Two-step extended Runge-Kutta-Nyström-type methods

UR - https://www.scopus.com/pages/publications/80052324915

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DO - 10.1016/j.cpc.2011.07.007

M3 - 文章

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SN - 0010-4655

VL - 182

SP - 2486

EP - 2507

JO - Computer Physics Communications

JF - Computer Physics Communications

IS - 12

ER -

Two-step extended RKN methods for oscillatory systems

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Keywords

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