Mathematics – Numerical Analysis
Scientific paper
2010-05-11
Mathematics
Numerical Analysis
19 pages, 7 figures; Sections 1, 2, and 6 sliglthly modified
Scientific paper
We introduce a new family of symplectic integrators depending on a real parameter. When the paramer is zero, 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 value of the parameter, the corresponding method remains symplectic and has order 2s-2: hence it may be interpreted as an order 2s-2 (symplectic) perturbation of the Gauss method. Under suitable assumptions, we show that the free parameter may be properly tuned, at each step of the integration procedure, so as to guarantee energy conservation in the numerical solution. The resulting symplectic, energy conserving method shares the same order 2s as the generating Gauss formula.
Brugnano Luigi
Iavernaro Felice
Trigiante Donato
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