Canonical Runge-Kutta methods. (English) Zbl 0675.34010
An integration procedure is called canonical if it generates a globally canonical map if applied to a Hamiltonian system. In this note the author characterizes all canonical Runge-Kutta methods for Hamiltonian systems of the form \(\dot x=H^ T_ y\), \(\dot y=-H^ T_ x\) with Hamiltonian H(x,y,t), \(x,y\in {\mathbb{R}}^ n\), \(t\in {\mathbb{R}}\).
Reviewer: S.Balint
MSC:
| 65J99 | Numerical analysis in abstract spaces |
| 37-XX | Dynamical systems and ergodic theory |
| 70H05 | Hamilton’s equations |
References:
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| [7] | F. M. Lasagni, in preparation, to appear in Numerische Mathematik. |
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