Time-Symmetric Discretization of the Harmonic Oscillator

Antippa, Adel F.; Dubois, Daniel

doi:10.1063/1.3527146

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Time-Symmetric Discretization of the Harmonic Oscillator

Antippa, Adel F.; Dubois, Daniel

2010 • In Dubois, Daniel (Ed.) COMPUTING ANTICIPATORY SYSTEMS

Peer reviewed

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https://hdl.handle.net/2268/89002

DOI
10.1063/1.3527146

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Keywords :

time-symmetric discretization; discrete harmonic oscillator; incursion; hyperincursion; orbital stability; energy conservation

Abstract :

[en] We explicitly and analytically demonstrate that simple time-symmetric discretization of the harmonic oscillator (used as a simple model of a discrete dynamical system), leads to discrete equations of motion whose solutions are perfectly stable at all time scales, and whose energy is exactly conserved. This result is important for both fundamental discrete physics, as well as for numerical analysis and simulation.

Disciplines :

Physics
Computer science
Mathematics

Author, co-author :

Antippa, Adel F.

Dubois, Daniel ; Université de Liège - ULiège > HEC-Ecole de gestion : UER > UER Opérations

Language :

English

Title :

Time-Symmetric Discretization of the Harmonic Oscillator

Publication date :

2010

Event name :

CASYS'09 - Ninth International Conference on Computing Anticipatory Systems

Event organizer :

CHAOS

Event place :

Liège, Belgium

Event date :

3-8 August 2009

By request :

Yes

Audience :

International

Main work title :

COMPUTING ANTICIPATORY SYSTEMS

Editor :

Dubois, Daniel ; Université de Liège - ULiège > HEC Liège : UER > UER Opérations

Publisher :

American Institute of Physics, Melville, New York, United States

Edition :

http://link.aip.org/link/?APCPCS/1303/121/1

ISBN/EAN :

978-0-7354-0858-6

Collection name :

AIP CONFERENCE PROCEEDINGS, VOLUME 1303, Daniel M. Dubois, Editor

Pages :

121-125

Peer reviewed :

Peer reviewed

Additional URL :

http://link.aip.org/link/?APCPCS/1303/121/1

Available on ORBi :

since 15 April 2011

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Bibliography

Antippa, A. F., and Dubois, D. M., International Journal of Computing Anticipatory Systems, 11, 141-153 (2002).
Antippa, A. F., and Dubois, D. M., "Anticipation, Orbital Stability, and Energy Conservation in Discrete Harmonic Oscillators," in Computing Anticipatory Systems: CASYS'03-Sixth International Conference, edited by D. M. Dubois, American Institute of Physics Conference Proceedings AIP CP 718, American Institute of Physics, Melville, New York, 2004, pp. 3-44.
Antippa, A. F., and Dubois, D. M., "The Dual Incursive System of the Discrete Harmonic Oscillator," in Computing Anticipatory Systems: CASYS'05-Seventh International Conference, edited by D. M. Dubois, American Institute of Physics Conference Proceedings AIP CP 839, American Institute of Physics, Melville, New York, 2006, pp. 11-64.
Antippa, A. F., and Dubois, D. M., "The Superposed Hyperincursive System of the Discrete Harmonic Oscillator," in Computing Anticipatory Systems: CASYS'05-Seventh International Conference, edited by D. M. Dubois, American Institute of Physics Conference Proceedings AIP CP 839, American Institute of Physics, Melville, New York, 2006, pp. 65-126.
Antippa, A. F., and Dubois, D. M., Journal of Mathematical Physics, 48, 012701 (2007).
Antippa, A. F., and Dubois, D. M., Journal of Mathematical Physics, 49, 032701 (2008).
Antippa, A. F., and Dubois, D. M., "Synchronous Discrete Harmonic Oscillator," in Computing Anticipatory Systems: CASYS'07-Eighth International Conference, edited by D. M. Dubois, American Institute of Physics Conference Proceedings AIP CP 1051, American Institute of Physics, Melville, New York, 2008, pp. 82-99.