Efficient symplectic Runge-Kutta methods

R.P.K. Chan; Hongyu Liu; Geng Sun

doi:10.1016/j.amc.2005.02.021

Efficient symplectic Runge-Kutta methods

R.P.K. Chan
, Hongyu Liu^*
, Geng Sun

^*Corresponding author for this work

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

9 Citations (Scopus)

Abstract

The present paper continues the research in [H.Y. Liu, G. Sun, Symplectic RK methods and symplectic PRK methods with real eigenvalues, J. Comput. Math. 22(5) (2004) 769-776] on symplectic Runge-Kutta (RK) methods with real eigenvalues. In a general setting, a new but simple proof of the main result in [H.Y. Liu, G. Sun, Symplectic RK methods and symplectic PRK methods with real eigenvalues, J. Comput. Math. 22(5) (2004) 769-776] is given that an s-stage, pth order such method must have that p ≤ s + 1 when s is odd, and p ≤ s when s is even. Then it is shown that in case s is odd, the maximum order is reachable. However, in comparison with composition method, the latter is superior in consideration of efficiency in high order. Some theoretically interesting properties of such methods are included. © 2005 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	908-924
Journal	Applied Mathematics and Computation
Volume	172
Issue number	2 SPEC. ISS.
Online published	18 Apr 2005
DOIs	https://doi.org/10.1016/j.amc.2005.02.021
Publication status	Published - 15 Jan 2006
Externally published	Yes
Event	The Beijing-HK Scientific Computing Meetings - Academy of Mathematics and Systems Science of Chinese Academy of Sciences, Beijing, China Duration: 13 Dec 2003 → 13 Dec 2003

Research Keywords

A-stability
Algebraically stable
Efficiency
Real eigenvalues
Runge-Kutta method
Symplectic

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10.1016/j.amc.2005.02.021

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title = "Efficient symplectic Runge-Kutta methods",

abstract = "The present paper continues the research in [H.Y. Liu, G. Sun, Symplectic RK methods and symplectic PRK methods with real eigenvalues, J. Comput. Math. 22(5) (2004) 769-776] on symplectic Runge-Kutta (RK) methods with real eigenvalues. In a general setting, a new but simple proof of the main result in [H.Y. Liu, G. Sun, Symplectic RK methods and symplectic PRK methods with real eigenvalues, J. Comput. Math. 22(5) (2004) 769-776] is given that an s-stage, pth order such method must have that p ≤ s + 1 when s is odd, and p ≤ s when s is even. Then it is shown that in case s is odd, the maximum order is reachable. However, in comparison with composition method, the latter is superior in consideration of efficiency in high order. Some theoretically interesting properties of such methods are included. {\textcopyright} 2005 Elsevier Inc. All rights reserved.",

keywords = "A-stability, Algebraically stable, Efficiency, Real eigenvalues, Runge-Kutta method, Symplectic",

author = "R.P.K. Chan and Hongyu Liu and Geng Sun",

year = "2006",

month = jan,

day = "15",

doi = "10.1016/j.amc.2005.02.021",

language = "English",

volume = "172",

pages = "908--924",

journal = "Applied Mathematics and Computation",

issn = "0096-3003",

publisher = "Elsevier Inc.",

number = "2 SPEC. ISS.",

note = "The Beijing-HK Scientific Computing Meetings ; Conference date: 13-12-2003 Through 13-12-2003",

}

TY - JOUR

T1 - Efficient symplectic Runge-Kutta methods

AU - Chan, R.P.K.

AU - Liu, Hongyu

AU - Sun, Geng

PY - 2006/1/15

Y1 - 2006/1/15

N2 - The present paper continues the research in [H.Y. Liu, G. Sun, Symplectic RK methods and symplectic PRK methods with real eigenvalues, J. Comput. Math. 22(5) (2004) 769-776] on symplectic Runge-Kutta (RK) methods with real eigenvalues. In a general setting, a new but simple proof of the main result in [H.Y. Liu, G. Sun, Symplectic RK methods and symplectic PRK methods with real eigenvalues, J. Comput. Math. 22(5) (2004) 769-776] is given that an s-stage, pth order such method must have that p ≤ s + 1 when s is odd, and p ≤ s when s is even. Then it is shown that in case s is odd, the maximum order is reachable. However, in comparison with composition method, the latter is superior in consideration of efficiency in high order. Some theoretically interesting properties of such methods are included. © 2005 Elsevier Inc. All rights reserved.

AB - The present paper continues the research in [H.Y. Liu, G. Sun, Symplectic RK methods and symplectic PRK methods with real eigenvalues, J. Comput. Math. 22(5) (2004) 769-776] on symplectic Runge-Kutta (RK) methods with real eigenvalues. In a general setting, a new but simple proof of the main result in [H.Y. Liu, G. Sun, Symplectic RK methods and symplectic PRK methods with real eigenvalues, J. Comput. Math. 22(5) (2004) 769-776] is given that an s-stage, pth order such method must have that p ≤ s + 1 when s is odd, and p ≤ s when s is even. Then it is shown that in case s is odd, the maximum order is reachable. However, in comparison with composition method, the latter is superior in consideration of efficiency in high order. Some theoretically interesting properties of such methods are included. © 2005 Elsevier Inc. All rights reserved.

KW - A-stability

KW - Algebraically stable

KW - Efficiency

KW - Real eigenvalues

KW - Runge-Kutta method

KW - Symplectic

UR - https://www.scopus.com/pages/publications/31644450405

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-31644450405&origin=recordpage

U2 - 10.1016/j.amc.2005.02.021

DO - 10.1016/j.amc.2005.02.021

M3 - RGC 21 - Publication in refereed journal

SN - 0096-3003

VL - 172

SP - 908

EP - 924

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 2 SPEC. ISS.

T2 - The Beijing-HK Scientific Computing Meetings

Y2 - 13 December 2003 through 13 December 2003

ER -

Efficient symplectic Runge-Kutta methods

Abstract

Research Keywords

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