We introduce a new family of symplectic integrators for canonical Hamiltonian systems depending on a real parameter α, which are able to preserve energy along any given trajectory. For α = 0, the corresponding method in the family becomes the classical Gauss collocation formula of order 2s, where s denotes the number of the internal stages. For any given non-null α, the corresponding method remains symplectic and has order 2s − 2: hence it may be interpreted as a O(h2s−2) (symplectic) perturbation of the Gauss method. Under suitable assumptions, we show that the parameter α may be properly tuned, at each step of the integration procedure, so as to guarantee energy conservation in the numerical solution, as well as to maintain the original order 2s as the generating Gauss formula.

ENERGY AND QUADRATIC INVARIANTS PRESERVING INTEGRATORS BASED UPON GAUSS COLLOCATION FORMULAE / L.Brugnano; F.Iavernaro; D.Trigiante. - In: SIAM JOURNAL ON NUMERICAL ANALYSIS. - ISSN 0036-1429. - STAMPA. - 50:(2012), pp. 2897-2916. [10.1137/110856617]

ENERGY AND QUADRATIC INVARIANTS PRESERVING INTEGRATORS BASED UPON GAUSS COLLOCATION FORMULAE

BRUGNANO, LUIGI;
2012

Abstract

We introduce a new family of symplectic integrators for canonical Hamiltonian systems depending on a real parameter α, which are able to preserve energy along any given trajectory. For α = 0, the corresponding method in the family becomes the classical Gauss collocation formula of order 2s, where s denotes the number of the internal stages. For any given non-null α, the corresponding method remains symplectic and has order 2s − 2: hence it may be interpreted as a O(h2s−2) (symplectic) perturbation of the Gauss method. Under suitable assumptions, we show that the parameter α may be properly tuned, at each step of the integration procedure, so as to guarantee energy conservation in the numerical solution, as well as to maintain the original order 2s as the generating Gauss formula.
2012
50
2897
2916
L.Brugnano; F.Iavernaro; D.Trigiante
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/680528
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