Finite Difference Method Of Several Types Of Non-local Boundary 2D Elliptic Problems

In this paper, the finite difference method of solving two-dimensional elliptic problems subject to given non-local boundary conditions is considered. Firstly, a brief overview of current development of non-local problem, and secondly, to discuss the finite difference method for solving four types of non-local boundary conditions Poisson equation. By constructing four types of non-discrete difference Scheme for elliptic problems local boundary conditions, with the discrete Fourier transform method to solve these four non-local elliptic problems by Taylor formula obtained discrete format local truncation error proof method of discrete Fourier transform convergence order of the error with a saturation. Finally, the results of numerical experiments with the four types of nonlocal elliptic problems with homogeneous and inhomogeneous boundary conditions, verify the correctness of our approach.