On the canonical property of maps generated by methods of Runge-Kutta type for integration of systems \(\ddot x=-\partial U/\partial x\). (Russian) Zbl 0686.65039

An explicit Runge-Kutta-Nyström method for Hamiltonian systems is studied. Necessary and sufficient conditions for the canonical property of the phase space in the initial problem to keep validity also in the approximate method are derived. It is shown this property is not valid if we use ordinary Runge-Kutta methods.
Reviewer: S.Gocheva-Ilieva


65L05 Numerical methods for initial value problems involving ordinary differential equations
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
34A34 Nonlinear ordinary differential equations and systems