Discretization of dynamical systems      with first integrals

Michal Fečkan; Michal Pospíšil

doi:10.3934/dcds.2013.33.3543

Article Contents

2013, Volume 33, Issue 8: 3543-3554. Doi: 10.3934/dcds.2013.33.3543

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Discretization of dynamical systems with first integrals

Michal Fečkan^1, and
Michal Pospíšil^2,

1.
Department of Mathematical Analysis and Numerical Mathematics, Comenius University, Mlynská dolina, 842 48 Bratislava
2.
Centre for Research and Utilization of Renewable Energy, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technická 3058/10, 616 00 Brno

Received: April 30, 2012

Revised: August 31, 2012

Published: July 2013

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Abstract

We find conditions under which the first integral of an ordinary differential equation becomes a discrete Lyapunov function for its numerical discretization. This result is applied for precluding periodic and bounded orbits under discretization for several cases.

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Mathematics Subject Classification: Primary: 34C25, 65L20; Secondary: 34C14.

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