To the top

Page Manager: Webmaster
Last update: 9/11/2012 3:13 PM

Tell a friend about this page
Print version

A minimal-variable symple… - University of Gothenburg, Sweden Till startsida
Sitemap
To content Read more about how we use cookies on gu.se

A minimal-variable symplectic method for isospectral flows

Journal article
Authors Milo Viviani
Published in BIT Numerical Mathematics
ISSN 0006-3835
Publication year 2019
Published at Department of Mathematical Sciences
Language en
Links dx.doi.org/10.1007/s10543-019-00792...
Subject categories Computational Mathematics

Abstract

Isospectral flows are abundant in mathematical physics; the rigid body, the the Toda lattice, the Brockett flow, the Heisenberg spin chain, and point vortex dynamics, to mention but a few. Their connection on the one hand with integrable systems and, on the other, with Lie–Poisson systems motivates the research for optimal numerical schemes to solve them. Several works about numerical methods to integrate isospectral flows have produced a large varieties of solutions to this problem. However, many of these algorithms are not intrinsically defined in the space where the equations take place and/or rely on computationally heavy transformations. In the literature, only few examples of numerical methods avoiding these issues are known, for instance, the spherical midpoint method on so(3). In this paper we introduce a new minimal-variable, second order, numerical integrator for isospectral flows intrinsically defined on quadratic Lie algebras and symmetric matrices. The algorithm is isospectral for general isospectral flows and Lie–Poisson preserving when the isospectral flow is Hamiltonian. The simplicity of the scheme, together with its structure-preserving properties, makes it a competitive alternative to those already present in literature.

Page Manager: Webmaster|Last update: 9/11/2012
Share:

The University of Gothenburg uses cookies to provide you with the best possible user experience. By continuing on this website, you approve of our use of cookies.  What are cookies?