A Higher Order Approximation Scheme on Lie Groups

被引：0

作者：

Mueller, Andreas ^{[1
]}

机构：

[1] Univ Duisburg Essen, Chair Mech & Robot, D-47057 Duisburg, Germany

来源：

NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, VOLS I-III | 2010年 / 1281卷

关键词：

Differential equations; Lie groups; approximation; time stepping schemes;

D O I：

暂无

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

This paper presents approximation formulae for approximating the solution of differential equitations = Omega(X)X on Lie groups. The approximation is given terms of time derivatives of vector field. A kth order approximation requires the first k - 1 time derivatives. The presented formulae are applicable when the vector field X is accessible, as for the velocity field of rigid bodies, but it can also be used to derive numerical time stepping schemes for solving the ODE.

引用

页码：1281 / 1283

页数：3

共 8 条

[1] NUMERICAL-INTEGRATION OF ORDINARY DIFFERENTIAL-EQUATIONS ON MANIFOLDS [J].

CROUCH, PE ;

GROSSMAN, R .

JOURNAL OF NONLINEAR SCIENCE, 1993, 3 (01) :1-33

[2]

Helgason S., 1978, DIFFERENTIAL GEOMETR

[3]

Iserles A., 2000, Acta Numerica, V9, P215, DOI 10.1017/S0962492900002154

[4]

Lubich C., 2010, Springer Series in Computational Mathematics, V31

[5] ON THE EXPONENTIAL SOLUTION OF DIFFERENTIAL EQUATIONS FOR A LINEAR OPERATOR [J].

MAGNUS, W .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1954, 7 (04) :649-673

[6] Approximation of finite rigid body motions from velocity fields [J].

Mueller, Andreas .

ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 2010, 90 (06) :514-521

[7] Runge-Kutta methods on Lie groups [J].

Munthe-Kaas, H .

BIT, 1998, 38 (01) :92-111

[8] Collocation and relaxed collocation for the FER and the magnus expansions [J].

Zanna, A .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1999, 36 (04) :1145-1182

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