Difference method of increased order of accuracy for the Poisson equation with nonlocal conditions (Q731579)

The author considers the two-dimension Poisson equation with nonlocal (integral) boundary conditions in one of the directions. He constructs a finite-difference scheme of fourth order approximations. He obtains a criterion for the nondegeneracy of the matrix of the system on finite-difference equations and conditions for its eigenvalues to be positive. The fact that all the eigenvalues are positive ensures the existence of a unique solution of the finite-difference problem and the convergence of a specific iteration method.