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Solving the wave equation on discrete time scales

Davis Funk and Charis Tsikkou
Vol. 19 (2026), No. 4, 693–707
DOI: 10.2140/involve.2026.19.693
Abstract

We present a solution to an initial value problem for the 1-dimensional wave equation on time scales by applying a Fourier transform and its inverse via contour integrals. The time scale of the spatial dimension is set to integers and a broader class of discrete time scales, while the time dimension is set to positive real numbers.

Keywords
partial dynamic equations, wave equation, time scales
Mathematical Subject Classification
Primary: 34N05, 35R07, 39A14
Milestones
Received: 15 October 2024
Revised: 18 February 2025
Accepted: 20 February 2025
Published: 13 October 2026

Communicated by Martin Bohner
Authors
Davis Funk
School of Mathematical and Data Sciences
West Virginia University
Morgantown, WV
United States
Charis Tsikkou
School of Mathematical and Data Sciences
West Virginia University
Morgantown, WV
United States
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