Finite Difference Method for a Second-Order Ordinary Differential Equation with a Boundary Condition of the Third Kind

Abstract

We present a second-order finite difference method for obtaining a solution of a second order two-point boundary value problem subject to Sturm's boundary conditions. We use equidistant discretization points, and the discretization of the differential equation at an interior point is based on just two evaluations of the function. Numerical examples are considered and the convergence of the proposed method is proved computationally. © 2010, Institute of Mathematics, NAS of Belarus. All rights reserved.