Runge-Kutta collocation methods for rigid body Lie-Poisson equations

被引：1
|
作者：
Ergenc, T
Karasozen, B
机构：
[1] Department of Mathematics, Middle East Technical University
来源：
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 1996年 / 62卷 / 1-2期
关键词：
Lie-Poisson system; one-forms; Euler top; Runge-Kutta methods;
D O I：
10.1080/00207169608804525
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The rigid body Lie-Poisson structure in three dimensions is considered. We show that the symplectic collocation type Runge-Kutta methods preserve the one-form of the underlying system. The linear error growth, energy and momentum conservation properties of the numerical solutions are discussed for Euler top equation.
引用
收藏
页码：63 / 71
页数：9
相关论文
共 50 条
  • [1] PERTURBED COLLOCATION AND RUNGE-KUTTA METHODS
    NORSETT, SP
    WANNER, G
    [J]. NUMERISCHE MATHEMATIK, 1981, 38 (02) : 193 - 208
  • [2] Runge-Kutta methods on Lie groups
    Hans Munthe-Kaas
    [J]. BIT Numerical Mathematics, 1998, 38 : 92 - 111
  • [3] Runge-Kutta methods on Lie groups
    Munthe-Kaas, H
    [J]. BIT, 1998, 38 (01): : 92 - 111
  • [4] Symmetric partitioned Runge-Kutta methods for differential equations on Lie groups
    Wandelt, M.
    Guenther, M.
    Knechtli, F.
    Striebel, M.
    [J]. APPLIED NUMERICAL MATHEMATICS, 2012, 62 (12) : 1740 - 1748
  • [5] Multi-symplectic Runge-Kutta collocation methods for Hamiltonian wave equations
    Reich, S
    [J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2000, 157 (02) : 473 - 499
  • [6] Stabilized starting algorithms for collocation Runge-Kutta methods
    González-Pinto, S
    Montijano, JI
    Pérez-Rodríguez, SP
    [J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2003, 45 (1-3) : 411 - 428
  • [7] Runge-Kutta collocation methods for differential-algebraic equations of indices 2 and 3
    L. M. Skvortsov
    [J]. Computational Mathematics and Mathematical Physics, 2012, 52 : 1373 - 1383
  • [8] Lie-Butcher theory for Runge-Kutta methods
    MuntheKaas, H
    [J]. BIT, 1995, 35 (04): : 572 - 587
  • [9] Runge-Kutta collocation methods for differential-algebraic equations of indices 2 and 3
    Skvortsov, L. M.
    [J]. COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2012, 52 (10) : 1373 - 1383
  • [10] Collocation-based two step Runge-Kutta methods for Ordinary Differential Equations
    D'Ambrosio, R.
    Ferro, M.
    Paternoster, B.
    [J]. COMPUTATIONAL SCIENCE AND ITS APPLICATIONS - ICCSA 2008, PT 2, PROCEEDINGS, 2008, 5073 : 736 - +
12345