On simulations of the classical harmonic oscillator equation by difference equations

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. Copyright © 2006 J. L. Cieśliński and B. Ratkiewicz.