A 5(3) pair of explicit ARKN methods for the numerical integration of perturbed oscillators

被引：37

作者：

Franco, JM ^{[1
]}

机构：

[1] Univ Zaragoza, CPS Ingn, Dept Matemat Aplicada, Zaragoza 50018, Spain

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2003年 / 161卷 / 02期

关键词：

adapted RKN methods; embedded pairs; oscillatory problems; RUNGE-KUTTA METHODS; INITIAL-VALUE PROBLEMS; POLYNOMIALS;

D O I：

10.1016/j.cam.2003.03.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A new embedded pair of explicit RKN methods specially adapted to the numerical integration of perturbed oscillators is obtained. This pair depends on a parameter nu = omegah > 0 (h is the integration step and omega is the dominant frequency), and it has four stages and algebraic orders five and three. The numerical experiments carried out show that the new pair is very competitive when it is compared with high-quality codes proposed in the scientific literature. (C) 2003 Elsevier B.V. All rights reserved.

引用

页码：283 / 293

页数：11

共 50 条

[1] A new pair of explicit ARKN methods for the numerical integration of general perturbed oscillators
Fang, Yonglei
Wu, Xinyuan
APPLIED NUMERICAL MATHEMATICS, 2007, 57 (02) : 166 - 175
[2] Stability of explicit ARKN methods for perturbed oscillators
Franco, JM
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2005, 173 (02) : 389 - 396
[3] One-step explicit methods for the numerical integration of perturbed oscillators
Li, Qinghong
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2011, 88 (15) : 3324 - 3334
[4] On Multidimensional ARKN methods for Systems of Perturbed Oscillators
Wu, Xinyuan
You, Xiong
NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, VOLS 1 AND 2, 2009, 1168 : 896 - +
[5] Trigonometrically-fitted ARKN methods for perturbed oscillators
Yang, Hongli
Wu, Xinyuan
APPLIED NUMERICAL MATHEMATICS, 2008, 58 (09) : 1375 - 1395
[6] Note on derivation of order conditions for ARKN methods for perturbed oscillators
Wu, Xinyuan
You, Xiong
Li, Jiyong
COMPUTER PHYSICS COMMUNICATIONS, 2009, 180 (09) : 1545 - 1549
[7] A Runge-Kutta-Nystrom pair for the numerical integration of perturbed oscillators
de Vyver, HV
COMPUTER PHYSICS COMMUNICATIONS, 2005, 167 (02) : 129 - 142
[8] 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
[9] An adapted explicit hybrid method of Numerov-type for the numerical integration of perturbed oscillators
Van de Vyver, Hans
APPLIED MATHEMATICS AND COMPUTATION, 2007, 186 (02) : 1385 - 1394
[10] Extended RKN-type methods for numerical integration of perturbed oscillators
Yang, Hongli
Wu, Xinyuan
You, Xiong
Fang, Yonglei
COMPUTER PHYSICS COMMUNICATIONS, 2009, 180 (10) : 1777 - 1794

← 1 2 3 4 5 →