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On a discrete version of the wave equation

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Abstract

The main purpose of this paper is to determine the general (and also the continuous) solutions of the discrete wave equation, that is, to solve the following partial difference equation

$$\underset{(x)}{\Delta^{2}_{1}}u(x, y)=\underset{(y)}{\Delta^{2}_{1}}u(x, y).$$

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Authors and Affiliations

  1. Department of Analysis, Institute of Mathematics, University of Debrecen, P. O. Box: 12, Debrecen, 4010, Hungary

    Eszter Gselmann

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  1. Eszter Gselmann
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Correspondence to Eszter Gselmann.

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Dedicated to Professor János Aczél on his 90th birthday

This research has been supported by the Hungarian Scientific Research Fund (OTKA) Grant NK 81402 and by the TÁMOP 4.2.4.A/2-11-1-2012-0001 (Nemzeti Kiválóság Program—Hazai hallgatói, illetve kutatói személyi támogatást biztosító rendszer kidolgozása és működtetése konvergencia program) project implemented through the EU and Hungary co-financed by the European Social Fund.

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Gselmann, E. On a discrete version of the wave equation. Aequat. Math. 89, 63–70 (2015). https://doi.org/10.1007/s00010-014-0278-2

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  • DOI: https://doi.org/10.1007/s00010-014-0278-2

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