D. J. Galiffa, University of Central Florida


On a Finite Difference Method for a Nonlocal Elliptic Boundary Value Problem

Abstract:  In 2005 Correa and Filho established existence and uniqueness results for a particular nonlinear PDE, which arises in physical models of thermodynamical equilibrium via Coulomb potential, among others. In this work we discuss a numerical method for a special case of this equation. We first consider the existence and uniqueness of the analytic problem using a fixed point argument and the contraction mapping theorem. Next, we evaluate the solution of the numerical problem via a finite difference scheme. From there, the existence and convergence of the approximate solution will be addressed as well as a uniqueness argument, which requires some additional restrictions. Finally, we conclude the work with some numerical examples where an interval-halving technique was implemented.

Joint work with: John Cannon (UCF)