Computational model of stationary flow with integral nonlocal boundary conditions

A finite-difference numerical method for solving the model represented by the Poisson equation with integral non-local boundary conditions is considered. The model describes the steady flow of fluid near the well under the condition of a known total flow both on the well contour and on the permeable part of the domain boundary. The model describes one of the possible situations in well-logged oil production. The problems of existence and uniqueness of the solution to this problem are discussed. Peaceman–Rachford type method used to construct a difference scheme.