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