Stochastic simulation algorithm for solving the system of Lame equations for two- and three-dimensional domains by combining the Slobodianskii representation, the method of fundamental solutions and a random projection method

In this paper, a new stochastic algorithm for solving the system of Lame equations based on the Slobodianskii representation is proposed, in which the recovery of boundary conditions for the harmonic functions involved is carried out implicitly using the method of fundamental solutions, while the unknown coefficients in this method are calculated using a stochastic projection method. Results of numerical experiments for several examples of two- and three-dimensional boundary value problems are presented, which demonstrate the high efficiency of the proposed method.