Development and application of a numerical method for solution of linear elliptic equations in unbounded region

In this work we propose a new method for solution of linear elliptic equations in unbounded domain. The method is based on representation of exact solution as a sum of two functions. The former is a solution of some auxiliary problem and the latter can be found using Green's formula. Using finite-difference schemes this method has quadratic order of accuracy, independent of the size of computational domain, and in 2d case requires $O(N^3)$ operations to find the solution, where $N^2$ — is the number of nodes within the computational domain. In 3d case the method requires $O(N^4)$ operations. Test computational examples are provided, showing the method’s efficiency.