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  • Research Article
  • Open Access

On simulations of the classical harmonic oscillator equation by difference equations

Advances in Difference Equations20062006:040171

  • Received: 29 October 2005
  • Accepted: 10 January 2006
  • Published:


We discuss the discretizations of the second-order linear ordinary diffrential equations with constant coefficients. Special attention is given to the exact discretization because there exists a difference equation whose solutions exactly coincide with solutions of the corresponding differential equation evaluated at a discrete sequence of points. Such exact discretization can be found for an arbitrary lattice spacing.


  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis
  • Functional Equation


Authors’ Affiliations

Instytut Fizyki Teoretycznej, Uniwersytet w Białymstoku, ul. Lipowa 41, Białystok, 15-424, Poland
Doctoral Studies, Wydział Fizyki, Uniwersytet Adama Mickiewicza, Poznań, Poland
I Liceum Ogólnokształcące, 16-300 Augustów, Osiedle śródmieście 31, Poland


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© J. L. Cieśliński and B. Ratkiewicz 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.