  This article investigates the velocity dispersion and the spurious reflection
of the viscoelastic wave that occur in the numerical integration of the
viscoelastic wave equation. For this purpose, the classic finite element of two
nodes, with a consistent and lumped mass model for spatial integration is
considered, and the Newmark average acceleration method of the two-step version
for integration over time is adopted. The resulting system of the difference
equation is then analytically integrated in non-finite terms (numerical
solution of waves) using complex notation. The numerical results reveal that,
even for a refined mesh, the dispersion and spurious reflections are
significant.
