Extended RKN-type methods for numerical integration of perturbed oscillators

被引：62
|
作者：
Yang, Hongli [1 ]
Wu, Xinyuan [1 ]
You, Xiong [1 ]
Fang, Yonglei [2 ]
机构：
[1] Nanjing Univ, Dept Math, State Key Lab Novel Software Technol, Nanjing 210093, Peoples R China
[2] Nanjing Normal Univ, Sch Math & Comp Sci, Nanjing 210097, Peoples R China
来源：
COMPUTER PHYSICS COMMUNICATIONS | 2009年 / 180卷 / 10期
关键词：
Extended tree theory; Order conditions; Runge-Kutta-Nystrom-type methods; Perturbed oscillators; INITIAL-VALUE PROBLEMS; EXPLICIT ARKN METHODS; PAIR;
D O I：
10.1016/j.cpc.2009.05.010
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
In this paper, extended Runge-Kutta-Nystrom-type methods for the numerical integration of perturbed oscillators with low frequencies are presented, which inherit the framework of RKN methods and make full use of the special feature of the true flows for both the internal stages and the updates. Following the approach of J. Butcher, E. Hairer and G. Warmer, we develop a new kind of tree set to derive order conditions for the extended Runge-Kutta-Nystrom-type methods. The numerical stability and phase properties of the new methods are analyzed. Numerical experiments are accompanied to show the applicability and efficiency of our new methods in comparison with some well-known high quality methods proposed in the scientific literature. (C) 2009 Elsevier B.V. All rights reserved.
引用
收藏
页码：1777 / 1794
页数：18
相关论文
共 50 条
  • [1] Extended RKN-type methods for numerical integration of perturbed oscillators (vol 180, pg 1777, 2009)
    Wu, Xinyuan
    COMPUTER PHYSICS COMMUNICATIONS, 2010, 181 (09) : 1658 - 1658
  • [2] Extended RKN-type methods with minimal dispersion error for perturbed oscillators
    Fang, Yonglei
    Ming, Qinghe
    Wu, Xinyuan
    COMPUTER PHYSICS COMMUNICATIONS, 2010, 181 (03) : 639 - 650
  • [3] On extended RKN integrators for multidimensional perturbed oscillators with applications
    Wu, Xinyuan
    Wang, Bin
    Shi, Wei
    You, Xiong
    APPLIED MATHEMATICAL MODELLING, 2012, 36 (04) : 1504 - 1513
  • [4] A new family of Runge–Kutta type methods for the numerical integration of perturbed oscillators
    Ana B. González
    Pablo Martín
    José M. Farto
    Numerische Mathematik, 1999, 82 : 635 - 646
  • [5] RKN-type parallel block PC methods with Lagrange-type predictors
    Hanoi Univ of Sciences, Hanoi, Viet Nam
    Comput Math Appl, 9 (45-57):
  • [6] RKN-type parallel block PC methods with Lagrange-type predictors
    Cong, NH
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1998, 35 (09) : 45 - 57
  • [7] Explicit symplectic RKN methods for perturbed non-autonomous oscillators: Splitting, extended and exponentially fitting methods
    Blanes, S.
    COMPUTER PHYSICS COMMUNICATIONS, 2015, 193 : 10 - 18
  • [8] Parallel block PC methods with RKN-type correctors and Adams-type predictors
    Cong, NH
    Minh, NTH
    INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2000, 74 (04) : 509 - 527
  • [9] A new family of Runge-Kutta type methods for the numerical integration of perturbed oscillators
    González, AB
    Martín, P
    Farto, JM
    NUMERISCHE MATHEMATIK, 1999, 82 (04) : 635 - 646
  • [10] Increasing the accuracy in the numerical integration of perturbed oscillators with new methods
    González, AB
    Martín, P
    García, A
    Farto, JM
    APPLIED NUMERICAL MATHEMATICS, 2002, 41 (02) : 295 - 304
12345