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On simulations of the classical harmonic oscillator equation by difference equations

Popular Physics 2007-05-23 v1 Computational Physics

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.

Keywords

Cite

@article{arxiv.physics/0507182,
  title  = {On simulations of the classical harmonic oscillator equation by difference equations},
  author = {Jan L. Cieslinski and Boguslaw Ratkiewicz},
  journal= {arXiv preprint arXiv:physics/0507182},
  year   = {2007}
}

Comments

17 pages plus 7 figures

R2 v1 2026-07-22T19:05:00.630Z