This article is cited in 1 paper

On Phenomenon of Scattering on Resonances Associated with Discretisation of Systems with Fast Rotating Phase

Anatoly Neishtadt^ab, Tan Su<sup>a

a</sup> Dept. of Math. Sciences, Loughborough University, Loughborough, Leicestershire LE11 3TU, UK
^b Space Research Institute (IKI), Profsoyuznaya ul. 84/32, Moscow 117997, Russia

Abstract: Numerical integration of ODEs by standard numerical methods reduces continuous time problems to discrete time problems. Discrete time problems have intrinsic properties that are absent in continuous time problems. As a result, numerical solution of an ODE may demonstrate dynamical phenomena that are absent in the original ODE. We show that numerical integration of systems with one fast rotating phase leads to a situation of such kind: numerical solution demonstrates phenomenon of scattering on resonances that is absent in the original system.

Keywords: systems with rotating phases, passage through a resonance, numerical integration, discretisation.

MSC: 34F15, 34C29, 65D30

Received: 16.03.2012
Accepted: 04.04.2012

Language: English

DOI: 10.1134/S1560354712030100

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