Stability Analysis of Finite-Difference Schemes for the Viscoelastic Wave Equation

It is difficult to predict stability properties of a finite difference scheme. It has to be investigated through the roots of the Z-transformed and Fourier transformed difference scheme (modal equation). To simultaneously investigate several schemes for the viscoelastic wave equation, it is possible to derive the modal equation with parameterized coefficients. Several conditionally stable schemes were found, where the most efficient is a staggered scheme with a stability condition closely resembling that of an elastic scheme