The finite-difference solution of mathematical-physics differential equations is carried out in two stages: 1) the writing of the difference scheme (a differ­ ence approximation to the differential equation on a grid), 2) the computer solution of the difference equations, which are written in the form of a high­ order system of linear algebraic equations of special form (ill- conditioned, band-structured). Application of general linear algebra methods is not always appropriate for such systems because of the need to store a large volume of information, as well as because of the large amount of work required by these methods. For the solution of difference equations, special methods