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
1Instytut Fizyki Teoretycznej, Uniwersytet w Białymstoku, ul. Lipowa 41, Białystok 15-424, Poland
2Doctoral Studies, Wydział Fizyki, Uniwersytet Adama Mickiewicza, Poznań, Poland
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.