Advances in Difference Equations
Volume 2006 (2006), Article ID 40171, 17 pages
doi:10.1155/ADE/2006/40171

On simulations of the classical harmonic oscillator equation by difference equations

Jan L. Cieśliński1 and Bogusław Ratkiewicz2,3

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

Received 29 October 2005; Accepted 10 January 2006

Copyright © 2006 Jan L. Cieśliński and Bogusław Ratkiewicz. 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.

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.