A new family of Runge-Kutta type methods for the numerical integration of perturbed oscillators

被引：57

作者：

González, AB ^{[1
]}

Martín, P ^{[1
]}

Farto, JM ^{[1
]}

机构：

[1] Univ Valladolid, ETS Ingenieros Ind, Dep Matemat Aplicada Ingn, E-47011 Valladolid, Spain

来源：

NUMERISCHE MATHEMATIK | 1999年 / 82卷 / 04期

关键词：

Mathematics Subject Classification (1991):65L05, 65L06;

D O I：

10.1007/s002110050434

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Our task in this paper is to present a new family of methods of the Runge-Kutta type for the numerical integration of perturbed oscillators. The key property is that those algorithms are able to integrate exactly, without truncation error, harmonic oscillators, and that, for perturbed problems the local error contains the perturbation parameter as a factor. Some numerical examples show the excellent behaviour when they compete with Runge-Kutta-Nystrom type methods.

引用

页码：635 / 646

页数：12

共 9 条

[1]

Bush A.W., 1992, Perturbation Methods for Engineers and Scientists

[2] THE DEVELOPMENT OF VARIABLE-STEP SYMPLECTIC INTEGRATORS, WITH APPLICATION TO THE 2-BODY PROBLEM [J].

CALVO, MP ;

SANZSERNA, JM .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 1993, 14 (04) :936-952

[3]

FAIREN V, 1994, COMPUT PHYS, V8, P455

[4]

FARTO JM, COMPUTER PHYSICS COM, V111, P110

[5]

HAIRER E., 1987, SOLVING ORDINARY DIF

[6] Multistep numerical methods based on the Scheifele G-functions with application to satellite dynamics [J].

Martin, P ;

Ferrandiz, JM .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1997, 34 (01) :359-375

[7]

Sanz- Serna J. M., 1994, NUMERICAL HAMILTONIA

[8] NUMERICAL INTEGRATION OF PERTURBED LINEAR OSCILLATING SYSTEMS [J].

SCHEIFELE, G .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 1971, 22 (01) :186-+

[9]

Verhulst Ferdinand, 1990, NONLINEAR DIFFERENTI, DOI 10.1007/978-3-642-97149-5

← 1 →