Journal
FOUNDATIONS OF COMPUTATIONAL MATHEMATICS
Volume 20, Issue 4, Pages 889-921Publisher
SPRINGER
DOI: 10.1007/s10208-019-09428-w
Keywords
Isospectral flow; Lie-Poisson integrator; Symplectic Runge-Kutta methods; Toda flow; Generalized rigid body; Chu's flow; Bloch-Iserles flow; Euler equations; Point vortices
Ask authors/readers for more resources
The theory of isospectral flows comprises a large class of continuous dynamical systems, particularly integrable systems and Lie-Poisson systems. Their discretization is a classical problem in numerical analysis. Preserving the spectrum in the discrete flow requires the conservation of high order polynomials, which is hard to come by. Existing methods achieving this are complicated and usually fail to preserve the underlying Lie-Poisson structure. Here, we present a class of numerical methods of arbitrary order for Hamiltonian and non-Hamiltonian isospectral flows, which preserve both the spectra and the Lie-Poisson structure. The methods are surprisingly simple and avoid the use of constraints or exponential maps. Furthermore, due to preservation of the Lie-Poisson structure, they exhibit near conservation of the Hamiltonian function. As an illustration, we apply the methods to several classical isospectral flows.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available