The natural boundary element (NBE) method is herein mainly adopted to compute the numerical solutions of the viscoelastic wave equation in a two-dimensional (2D) unbounded domain. To this end, a new time semi-discrete (TSD) scheme is constructed for the viscoelastic wave equation, and the existence, stability, and error estimates of the time semi-discretized solutions are analyzed. Subsequently, based on the natural boundary naturalization principle, a fully discrete NBE scheme is established. The existence and stability of the fully discrete NBE solutions are examined, and the errors between the analytical solution and the fully discrete NBE solutions are estimated. Finally, several numeric... More >