  A numerical method for the Dirichlet initial boundary value problem for the
elastic equation in the exterior and unbounded region of a smooth closed simply
connected 2-dimensional domain, is proposed and investigated. This method is
based on a combination of a Laguerre transformation with respect to the time
variable and a boundary integral equation approach in the spatial variables.
Using the Laguerre transformation in time reduces the time-depended problem to
a sequence of stationary boundary value problems, which are solved by a
boundary layer approach resulting to a sequence of boundary integral equations
of the first kind. The numerical discretization and solution are obtained by a
trigonometrical quadrature method. Numerical results are included.
