On the numerical solution of some nonlinear and nonlocal BVPs

The modeling of various physical questions in plasma kinetics and heat conduction lead to nonlinear boundary value problems involving a nonlocal operator, such as the integral of the unknown solution, which depends on the entire function in the domain rather than at a single point. This talk concerns a particular nonlocal boundary value problem recently studied in [1] by J.R.Cannon and D.J.Galiffa, who proposed a numerical method based on an interval-halving scheme. Starting from their results, we provide a more general convergence theorem and suggest a different iterative procedure to handle the nonlinearity of the discretized problem. References: [1] J.R.Cannon, D.J.Galiffa (2011) On a numerical method for a homogeneous, nonlinear, nonlocal, elliptic boundary problem, Nonlinear Analysis, Vol. 74, pp. 1702-1713.