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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Vydáno v:Journal of numerical analysis and approximation theory Ročník 54; číslo 1; s. 3 - 25
Hlavní autoři: Ait ichou, Mohamed, Ezziani, Abdelaaziz
Médium: Journal Article
Jazyk:angličtina
Vydáno: Publishing House of the Romanian Academy 30.06.2025
Témata:
Caputo fractional derivative
Finite-difference method
Viscoelastic
wave simulations
ISSN:2457-6794, 2501-059X
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Shrnutí: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