A stable finite difference scheme for fractional viscoelastic wave propagation in space-time domain

Authors

  • Mohamed Ait ichou EMA Team, LRST Laboratory, ESEFA, Ibnou Zohr University of Agadir, Morocco https://orcid.org/0000-0001-6635-8505
  • Abdelaaziz Ezziani Laboratory MAEGE , Hassan II University of Casablanca, Morocco

DOI:

https://doi.org/10.33993/jnaat541-1530

Keywords:

Caputo fractional derivative, wave simulations, Viscoelastic, Finite-difference method
Abstract views: 186

Abstract

This work focuses on the numerical approximation of the one dimensional wave propagation equation in a viscoelastic medium modelled by the fractional Zener model. First, we propose an explicit centred finite difference scheme. Then, we prove a sufficient stability condition for this scheme using an energy technique. Furthermore, we demonstrate that this condition is numerically necessary. Finally, we present various numerical simulations to validate the proposed scheme.

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Published

2025-06-30

Issue

Vol. 54 No. 1 (2025)

Section

Articles

License

Copyright (c) 2025 Mohamed Ait ichou, Abdelaaziz Ezziani

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

How to Cite

Ait ichou, M., & Ezziani, A. (2025). A stable finite difference scheme for fractional viscoelastic wave propagation in space-time domain. J. Numer. Anal. Approx. Theory, 54(1), 3-25. https://doi.org/10.33993/jnaat541-1530