A finite difference method for the singularly perturbed problem with nonlocal boundary condition

The purpose of this paper is to present a finite difference method for numerical solutions of singularly perturbed boundary value problem for second order ordinary differential equation with nonlocal boundary condition. By the method of integral identities with the use exponential basis functions and interpolating quadrature rules with the weight and remainder term in integral form an exponentially fitted difference scheme on an uniform mesh is developed which is shown to be original ε-uniformly first order accurate in the discrete maximum norm for original problem. Numerical results are presented, which illustrate the theoretical results.