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 operations to find the solution, where - is the number of nodes within the computational domain. In 3d case the method requires operations. Test computational examples are provided, showing the method’s efficiency.

Mathematical problems and theory of numerical methods