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In the paper, the R-function theory developed by Rvachew is applied to solve 2D elliptic boundary value problems. Unlike the well-established FEM or BEM method, this method requires dividing the solution into two parts. In the first part, the boundary conditions are satisfied exactly and in the second part, the differential equation is satisfied in an approximate way. In such a way, it is possible to formulate in one algorithm the so-called general structural solution of a boundary-value problem and use it for an arbitrary domain and arbitrary boundary conditions. The usefulness of the proposed computational method is verified using the example of the solution of the Laplace equation with mixed boundary conditions.

Application of R-Functions Method and Parallel Computations to the Solution of 2D Elliptic Boundary Value Problems