New absorbing boundary conditions for the finite difference method based on discrete solutions of Laplace equation

This work investigates the use of discrete solutions of Laplace equation to generate new absorbing boundary conditions for the Finite Difference Method.. The study is performed by solving the numerical difference equation analytically. These solutions show some useful characteristics that prove to be useful for the design of special boundaries. A particular use of special boundaries is the simulation of infinite size meshes. In this work, the behavior of the common four-point finite difference scheme for the Laplace equation is studied. Another interesting result is a parameter that can define the amount of iterations necessary to achieve a given error. The work is validated by comparison between the discrete solutions and numerical results.