Cost efficient Lie group integrators in the RKMK class

被引：10
作者：
Casas, F [1 ]
Owren, B
机构：
[1] Univ Jaume 1, Dept Matemat, Castellon de La Plana 12071, Spain
[2] NTNU, Dept Math Sci, N-7491 Trondheim, Norway
[3] Ctr Adv Study, N-0271 Oslo, Norway
来源：
BIT NUMERICAL MATHEMATICS | 2003年 / 43卷 / 04期
关键词：
time-integration; geometric integration; numerical integration of ordinary differential equations on manifolds; numerical analysis; Lie algebras; Lie groups;
D O I：
10.1023/B:BITN.0000009959.29287.d4
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
In this work a systematic procedure is implemented in order to minimise the computational cost of the Runge-Kutta-Munthe-Kaas (RKMK) class of Lie-group solvers. The process consists of the application of a linear transformation to the stages of the method and the analysis of a graded free Lie algebra to reduce the number of commutators involved. We consider here RKMK integration methods up to order seven based on some of the most popular Runge-Kutta schemes.
引用
收藏
页码：723 / 742
页数：20
相关论文
共 10 条
  • [1] Optimization of Lie group methods for differential equations
    Blanes, S
    Casas, F
    [J]. FUTURE GENERATION COMPUTER SYSTEMS-THE INTERNATIONAL JOURNAL OF ESCIENCE, 2003, 19 (03): : 331 - 339
  • [2] High order optimized geometric integrators for linear differential equations
    Blanes, S
    Casas, F
    Ros, J
    [J]. BIT NUMERICAL MATHEMATICS, 2002, 42 (02) : 262 - 284
  • [3] Butcher J. C., 1987, The Numerical Analysis of Ordinary Differential Equations: Runge-Kutta and General Linear Methods
  • [4] CASAS F, 2002, 52002 NORW U SCI TEC
  • [5] Complexity theory for Lie-group solvers
    Celledoni, E
    Iserles, A
    Norsett, SP
    Orel, B
    [J]. JOURNAL OF COMPLEXITY, 2002, 18 (01) : 242 - 286
  • [6] Hairer E., 2008, Solving Ordinary Differential Equations I Nonstiff problems
  • [7] On the solution of linear differential equations in Lie groups
    Iserles, A
    Norsett, SP
    [J]. PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1999, 357 (1754): : 983 - 1019
  • [8] Iserles A., 2000, Acta Numerica, V9, P215, DOI 10.1017/S0962492900002154
  • [9] Computations in a free Lie algebra
    Munthe-Kaas, H
    Owren, B
    [J]. PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1999, 357 (1754): : 957 - 981
  • [10] High order Runge-Kutta methods on manifolds
    Munthe-Kaas, H
    [J]. APPLIED NUMERICAL MATHEMATICS, 1999, 29 (01) : 115 - 127
1