A numerical algorithm for the analysis of viscoelastic waves in the Kelvin–Voigt medium

A numerical algorithm for solving dynamic problems in the theory of the viscoelastic Kelvin–Voigt medium is proposed on the basis of Ivanov's method of constructing difference schemes with prescribed dissipative properties. In the one-dimensional case, the numerical results are compared with the exact solution describing the propagation of plane monochromatic waves. When solving two-dimensional problems, the summary approximation method and the splitting method with respect to the spatial variables are applied. The algorithm is tested by solving the problem of traveling surface waves. For illustration of the method's efficiency, the Lamb's problem on the instantaneous action of a concentrated force at the boundary of a half-plane is solved in a viscoelastic formulation.