On simulations of the classical harmonic oscillator equation by difference equations

Jan L. Cieslinski; Boguslaw Ratkiewicz

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On simulations of the classical harmonic oscillator equation by difference equations

Jan L. Cieslinski·Boguslaw Ratkiewicz

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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.

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Jan L. Cieslinski, Boguslaw Ratkiewicz. 2005-07-26. On simulations of the classical harmonic oscillator equation by difference equations. https://arxiv.org/abs/physics/0507182

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