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Mathematics > Dynamical Systems

arXiv:1604.01215 (math)
[Submitted on 5 Apr 2016]

Title:Vibrational resonance: a study with high-order word-series averaging

Authors:Ander Murua, J.M. Sanz-Serna
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Abstract:We study a model problem describing vibrational resonance by means of a high-order averaging technique based on so-called word series. With the tech- nique applied here, the tasks of constructing the averaged system and the associ- ated change of variables are divided into two parts. It is first necessary to build recursively a set of so-called word basis functions and, after that, all the required manipulations involve only scalar coefficients that are computed by means of sim- ple recursions. As distinct from the situation with other approaches, with word- series, high-order averaged systems may be derived without having to compute the associated change of variables. In the system considered here, the construction of high-order averaged systems makes it possible to obtain very precise approxima- tions to the true dynamics.
Subjects: Dynamical Systems (math.DS); Numerical Analysis (math.NA); Computational Physics (physics.comp-ph)
Cite as: arXiv:1604.01215 [math.DS]
  (or arXiv:1604.01215v1 [math.DS] for this version)
  https://doi.org/10.48550/arXiv.1604.01215

Submission history

From: Jesus Maria Sanz-Serna [view email]
[v1] Tue, 5 Apr 2016 10:49:11 UTC (94 KB)
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