Perturbed collocation and symplectic RKN methods
Copyright policy )Perturbed collocation and symplectic RKN methods
It is shown that, within the class of Runge-Kutta-Nyström collocation methods, only the method of maximal order \(p = 2s\) is symplectic. By extending the idea of perturbed collocation proposed by \textit{S. P. Nørsett} and \textit{G. Wanner} [Numer. Math. 38, 193-208 (1981; Zbl 0471.65045)]to Nyström methods, new classes of symplectic methods or the orders \(2s - 1\) and \(2s - 2\) are derived.
- University of Cambridge United Kingdom
Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations, symplectic methods, Runge-Kutta-Nyström collocation methods, Nonlinear ordinary differential equations and systems, Numerical methods for initial value problems involving ordinary differential equations, perturbed collocation, method of maximal order
Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations, symplectic methods, Runge-Kutta-Nyström collocation methods, Nonlinear ordinary differential equations and systems, Numerical methods for initial value problems involving ordinary differential equations, perturbed collocation, method of maximal order
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