Development and application of numerical methods for solving tasks in unlimited regions based on the third Green formula

The two-step algorithm for solving problems with a linear elliptic operator, for which the fundamental solution is known, is analyzed. New methods for solving problems in an unbounded areas with a mixed type operator are proposed: a method for expanding a domain, a method for specifying of integral boundary conditions and a three-step iterative method. The range of applicability of the constructed methods is limited by cases where outside a certain finite area the operators have a known fundamental solution and their right-hand side is homogeneous. To solve specific problems on the basis of the proposed methods, computational algorithms have been created, implemented in the form of computer software. A series of computational experiments confirming the correctness of the methods carried out. The results of calculations of the electromagnetic field around the rails of an electrodynamic rail-type accelerator in the two-dimensional case are presented.