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 energy technique. Furthermore, we demonstrate that this condition is numerically necessary. Finally, we present various numerical simulations to validate the proposed scheme.