About Artificial Boundary Conditions for Difference Approximation of Helmholtz Equation

The difference approximation of a boundary problem on a half-plane for Helmholtz equation in stratified medium is considered. Artificial boundary conditions are constructed on a grid boundary of some domain that contains a support of a function in the right side of the equation. The construction of the artificial boundary conditions is based on the difference potentials method. Proofs of the respective theorems are presented in the paper.