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Theory and Modern Applications

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.

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Correspondence to Jan L Cieśliński.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Cieśliński, J.L., Ratkiewicz, B. On simulations of the classical harmonic oscillator equation by difference equations. Adv Differ Equ 2006, 040171 (2006). https://doi.org/10.1155/ADE/2006/40171

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