On simulations of the classical harmonic oscillator equation by difference equations

Details On simulations of the classical harmonic oscillator equation by difference equations On simulations of the classical harmonic oscillator equation by difference equations

2005-07-26

arxiv.org/abs/physics/0507182v1

Physics

Popular Physics

17 pages plus 7 figures

Scientific paper

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.

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