Second-Order Accurate Finite-Difference Scheme for Solving the Problem of Elastic Wave Diffraction by the Anisotropic Gradient Layer

Abstract

The boundary value problem for the Lame equations for the problem of elastic wave diffraction by an anisotropic layer with continuously varying elastic parameters is considered. The original problem is reduced to the boundary value problem for a system of ordinary differential equations of the given form. The finite-difference scheme is obtained by the method of approximation of integral identities. The theorem is proved that the error of approximation of the solution has a second order of accuracy for sufficiently continuous values of the elements of the elasticity tensor. Numerical results confirming theoretical conclusions are given.