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

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...

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Bibliographic Details
Published in:	Journal of numerical analysis and approximation theory Vol. 54; no. 1; pp. 3 - 25
Main Authors:	Ait ichou, Mohamed, Ezziani, Abdelaaziz
Format:	Journal Article
Language:	English
Published:	Publishing House of the Romanian Academy 30.06.2025
Subjects:	Caputo fractional derivative Finite-difference method Viscoelastic wave simulations
ISSN:	2457-6794, 2501-059X
Online Access:	Get full text
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Summary:	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.
ISSN:	2457-6794 2501-059X
DOI:	10.33993/jnaat541-1530