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

页码：1777 / 1794

页数：18

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