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  • Research Article
  • Open Access

On simulations of the classical harmonic oscillator equation by difference equations

Advances in Difference Equations20062006:040171

https://doi.org/10.1155/ADE/2006/40171

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

Abstract

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.

Keywords

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

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Authors’ Affiliations

(1)
Instytut Fizyki Teoretycznej, Uniwersytet w Białymstoku, ul. Lipowa 41, Białystok, 15-424, Poland
(2)
Doctoral Studies, Wydział Fizyki, Uniwersytet Adama Mickiewicza, Poznań, Poland
(3)
I Liceum Ogólnokształcące, 16-300 Augustów, Osiedle śródmieście 31, Poland

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