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A substitution law for B-series vector fields

Abstract : In this paper, we derive a new composition law obtained by substituting a B-series into the vector field appearing in another B-series. We derive explicit formulas for the computation of this law and study its algebraic properties. We then focus on the specific case of Hamiltonian vector fields. It is shown that this new law allows a convenient derivation of the modified equation occurring in backward error analysis or in numerical methods based on generating functions.
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Submitted on : Friday, May 19, 2006 - 8:42:57 PM
Last modification on : Monday, February 15, 2021 - 10:42:40 AM
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  • HAL Id : inria-00070509, version 1


Philippe Chartier, Ernst Hairer, Gilles Vilmart. A substitution law for B-series vector fields. [Research Report] RR-5498, INRIA. 2005, pp.24. ⟨inria-00070509⟩



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