Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Existence of Energy-Preserving Symplectic Integrators Based upon
  Gauss Collocation Formulae   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.

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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: cs
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The categories of this paper are: ao-sci
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph