Abstract: 

In this paper we consider an explicit finite difference scheme to solve an ill-posed continuation problem for the 3D wave equation with the data given on the part of the boundary. We reduce the problem to a system of linear algebraic equations and implement the numerical solution using an iterative solver and discuss an efficient solution to a dense system of linear equations. We use the Jacobi iteration method for solving the linear system to improve computational efficiency and the results of convergence of the proposed method. Numerical experiments are presented.