Numerical Integration of Lie-Poisson Systems while Preserving Coadjoint Orbits and Energy

In this paper we apply geometric integrators of the RKMK type to the problem of integrating Lie-Poisson systems numerically. By using the coadjoint action of the Lie group G on the dual Lie algebra$\mathprak{g}^\ast$to advance the numerical flow, we devise methods of arbitrary order that automatical...

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Bibliographic Details
Published in:	SIAM journal on numerical analysis Vol. 39; no. 1; pp. 128 - 145
Main Authors:	Engø, Kenth, Faltinsen, Stig
Format:	Journal Article
Language:	English
Published:	Philadelphia, PA Society for Industrial and Applied Mathematics 2002
Subjects:	Algebra Algorithms Applied mathematics Classical and quantum physics: mechanics and fields Classical mechanics of discrete systems: general mathematical aspects Coordinate systems Differential equations Energy Exact sciences and technology Lie groups Mathematical analysis Mathematical integration Mathematics Numerical analysis Numerical analysis. Scientific computation Numerical methods Orbits Ordinary differential equations Physics Rigid structures Sciences and techniques of general use Trapezoidal rule Truncation Euler equation Action Error estimation Iteration Machine System Truncation Time dependence Conservation law Numerical computation Energy Coadjoint orbit Orbit determination Integrator Lie Poisson equation Skew symmetric matrix Growth of error Rigid bodies Dimensionality Numerical integration Orbit Poisson equation Algorithm Flow Two dimensional equation Hamilton equation First integral Linear algebra Hamiltonian system Lie group Incompressible fluid Lie algebra
ISSN:	0036-1429, 1095-7170
Online Access:	Get full text
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