On simulations of the classical harmonic oscillator equation by difference equations
arXiv:physics/0507182
Abstract
We show that any second order linear ordinary diffrential equation with constant coefficients (including the damped and undumped harmonic oscillator equation) admits an exact discretization, i.e., there exists a difference equation whose solutions exactly coincide with solutions of the corresponding differential equation evaluated at a discrete sequence of points (a lattice). Such exact discretization is found for an arbitrary lattice spacing.
17 pages plus 7 figures