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On simulations of the classical harmonic oscillator equation by difference equations

Advances in Difference Equations volume 2006, Article number: 040171 (2006) Cite this article

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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Authors and Affiliations

  1. Instytut Fizyki Teoretycznej, Uniwersytet w Białymstoku, ul. Lipowa 41, Białystok, 15-424, Poland

    Jan L Cieśliński

  2. Doctoral Studies, Wydział Fizyki, Uniwersytet Adama Mickiewicza, Poznań, Poland

    Bogusław Ratkiewicz

  3. I Liceum Ogólnokształcące, 16-300 Augustów, Osiedle śródmieście 31, Poland

    Bogusław Ratkiewicz

Authors
  1. Jan L Cieśliński
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  2. Bogusław Ratkiewicz
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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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